From Hunter, S.J.: Outilines of Dogmatic Theology,

186. Soul and Body of the Church. But when the
Church is compared to a body, it must be remem-
bered that this is a living body, for the Church is
not a dead corpse. Now, we know that in a living
man there is a material body informed by a spiritual
soul : the body considered as being apart from the
soul is dead, while the soul is essentially living ; but
we have not the full life of a man unless soul and
body are fittingly united together. From these con-
siderations we are led to inquire whether there is
anything in the Church that corresponds to the soul
and body of a living man. Now the body, con-
sidered as a mere mass of matter, is equally ready
for many purposes ; it is the union with a human
soul which determines it as being a body of a man.
In the same way, a society is a collection of men,
but there must be something beside and beyond the
fact that a number of men are gathered together
that determines them as being a society of this or
that character : there must be some end which it is
proposed to attain by association, and some spirit
permeating the society, and leading each of its
members so to shape his individual conduct as more
or less to promote this end. It will often be difficult
to put into words what it is that constitutes this
spirit, and it will sometimes be yet harder to feel
assured how far it is partaken of by all those who in
outward semblance belong to the society ; also, we
often have reason to believe that the spirit exists in
some men who do not, in a material sense, belong
to the association. This is well seen in the case of
a nation. There is some principle, some sameness
of spirit, which unites all men who are entitled to
be called Englishmen, although it might be hard to
state with fulness and precision what elements are
found in this spirit. Regularly and in the bulk of
cases the possession of this spirit goes along with
birth and residence in England ; and in a certain
true sense, all in whom this material element is
found may be called Englishmen. But not in the
lull sense ; for there is little doubt that there are
persons resident in England who are wholly devoid
of the English spirit : who make to themselves an
end diverse from the end of the English nation, and
whose action is directed to the attainment of the
end which they have proposed to themselves ; while,
on the other hand, there may be persons resident in
other countries who are full of a spirit which is, in
fact, the English spirit whether they are aware of it
or not. On these principles we can distinguish the
soul and the body of the English nation. The
external fact of residence marks who belong to the
body ; possession of the spirit makes the man
belong to the soul : regularly, the soul and the
body are composed of the same persons ; but excep-
tionally, there may be persons belonging to the soul
who belong not to the body, and belonging to the
body who belong not to the soul.

In exactly the same way we speak of the Soul
and the Body of the Church. The Church is a
society of men instituted by Christ, and having for
its end to lead and enable men to avail themselves
of the redemption of the human race wrought by
the Founder ; and this society is as we have seen
(n. 168) visible: it has an external organization.
But it is important to know whether the possession
of the spirit is co-extensive -with the outward organi-
zation, or whether, on the other hand, the spirit
may in some instances be found beyond the bounds
of the organization, while in other instances it is
lacking within those bounds. In other words, we
must inquire what constitutes membership of the
Soul of the Church, and who they are that are
members of the Body.

187. Who belong to the Soul. From the explana-
tion given it follows without difficulty that they, and
they only, belong to the Soul of the Church who,
if the question were now to be settled, would be
found to have secured to themselves the fruits of
the Redemption ; to have the spiritual life abun-
dantly that Christ came to give (St. John x. 10) ; to
be partakers of the Divine Nature (2 St. Peter i. 4),
as St. Peter speaks : for these only are fit to pass to
that union with God which constitutes the state of
the Blessed ; in other words, the Just and the Just
alone constitute the Soul of the Church, (n. 184, II.)

It will be seen that membership of the Soul of
the Church is a present fact, and is independent of
past and future ; he that is a member of it may
cease to be so by Sin, he that is not a member may
become so by Justification, (n. 184, IV.) Exactly
the same is true of nations : he that is now full
of English spirit which actuates him in all his
conduct may once have been the determined enemy
of England, and may hereafter again take up this
spirit of enmity. It follows that there may be
some of the Predestined who do not now belong to
the Soul of the Church, and some who now belong
to that Soul but are not of the number of the
Predestined.

We have been speaking so far of the fulness of
membership of the Soul of the Church ; but it is
certain that many who are not of the number of the
Just nevertheless are receiving something of the
benefit of the Redemption, for they receive grace
which tends to lead them to Justification, and
without which they cannot be justified, as will be
seen in the Treatise on Grace : these, then, may be
said to belong to the Soul of the Church, but in an
imperfect sense.

It will be observed that there are no outward
means of telling, except by mere conjecture, what
men do belong to the Soul of the Church, and what
men do not belong to it : neither have we any
information, beyond conjecture, what proportion of
mankind belong to it at any given instant. God
has reserved to Himself this knowledge and the
knowledge of the number of the Predestined.
(2 Timothy ii. 19, and the Secret said in the
Mass during Lent.)

Fr. Hunter obviously does not envisage an invisible Church without a visible Body.

However, just as Fr. Fenton explained the true sense of St. Bellarmine’s exposition on the “Soul of the Church” in relation to the Catechumen, the same explanation can be applied here (we’ll save that for another time!).

From St. Robert Bellarmine, De Ecclessia Militante (as quoted in Monsignor Fenton's article, referred to by MRyan)

Again, some are of the soul, and not of the body, as catechumens or excommunicated persons, if they express faith and charity as they very well may.

http://www.strobertbellarmine.net/fenton/The%20Use%20of%20the%20terms%20Body%20and%20Soul%20with%20Reference%20to%20the%20Catholic%20Church.pdf

A man is inwardly united to Christ in so far as he elicits some supernatural
activity stemming from the gratia capitalis of our Lord Himself. No man can
have the supernatural life, or even the beginning of that life as found in faith
without charity, unless it be communicated to him by Christ. Thus there is a
necessary contact between our Lord and every man who falls within the category
of those who are "of the soul of the Church." But this union is invisible and inward,
brought about in and through the communication of divine grace.
The outward union with Christ is the factor by which a man places himself in
the ranks of the Church militant. The Church, as a society, is the body of Christ,
and thus the man who is a part of this society is actually joined to our Lord. The
persons who are "of the body of the Church" according to the terminology of St.
Robert, are precisely those who fulfill the minimum and essential requisites for
being parts of this society, and who thus are outwardly and visibly in contact with
Christ.

St. Robert offers catechumens and excommunicated persons as examples of
those who are not of the body of the Church, but who may be of the soul. He
teaches explicitly that such people are not members of the Catholic Church.12
Yet, far from postulating the existence of some spiritual and invisible society or
Church, in any manner distinct from the Catholic Church, to which such persons
would belong and through which they could achieve their eternal salvation, St.
Robert teaches distinctly that they can be saved by being of the Church by
desire.13

Thus there is one, and only one necessary social vehicle of salvation.

duckbill wrote:I really can't believe you guys are defending the condemned error of belonging to the "soul of the church" without belonging to the body!

Rasha is right this theory was condemned by Leo XIII and Pius XI did a follow-up because people like you were still promoting it after he condemned it:

Pope Pius XI, Mortalium Animos, Jan. 6, 1928, #10:
“For since the mystical body of Christ, in the same manner as His physical body, is one, compacted and fitly joined together, it were foolish and out of place to say that the mystical body is made up of members which are disunited and scattered abroad: whosoever therefore is not united with the body is no member of it, neither is he in communion with Christ its head.”
http://www.papalencyclicals.net/Pius11/P11MORTA.HTM

In individual cases, however in numbers known only to God, validly baptized persons might not be guilty of the sins of heresy and/or schism, owing to "invincible ignorance"( non-culpible ignorance) of the true Faith, Canon 5 in these cases they may belong to the Catholic Church by desire, provided they put no obstacle of the will to the authority of the Vicar of Christ, and obey God in things revealed for salvation such as being free from all mortal sin, and believe explicitly the mysteries of the faith which are necessary by a necessity of means, especially the mysteries of the Trinity and the Incarnation for salvation. (Note 7)

Pertaining to the Church's soul are (1) the sacramental powers of Baptism, of Confirmation, and of Order; (2) the jurisdictional power itself along with the right orientation it bestows on all those who listen to it with faith and obedience; and (3) sacramental grace. In other words, the powers of order and of jurisdiction, conferred first on the Apostles and handed down without a break to our times, are a constitutive and permanent element in the created soul of the Church; which soul, by structural necessity, is therefore hierarchized or apostolic.

Protestantism, prompt to dissociate invisible realities from visible, answered that there exists an "invisible Church" to which the just of all times belong, and a "visible Church" (or many visible Churches) which nobody is bound to enter. A certain number of Catholic writers, without wishing to dislocate the Church in this manner, imagined that her soul, i. e. sanctifying grace as they said, extended far beyond the limits of her body. They added that the just who in good faith remain ignorant of the Church, belong to the soul of the Church, and are therefore not outside her.

In the first place, however, such a mode of distinguishing the soul and body of the Church is without foundation in the authentic documents of the magisterium. It would seem to have been influenced by the Protestant conception of a "spiritual Church", distinct from the "visible Church", and its use appears to be dangerous. On the other hand we can easily see that the soul of the Church is not sanctifying grace pure and simple, as found in those who remain ignorant of the Church in good faith, but sanctifying grace as transmitted by the sacramental power and ruled by the jurisdictional power.

I do not say that there is no supernatural life at all outside the Church, but simply that there is none that does not look towards her. As preliminary to a deeper study of the soul of the Church, let us examine more closely the position of the just "outside".

1. The just of the first category [from those groups which lack the sacraments, or are separated from the Church, but have genuine sacraments] enjoy supernatural life—i. e. sanctifying grace issuing in the infused virtues and the gifts of the Holy Spirit. The whole tendency of this life is to grow towards completion, to enrich itself with those modalities which grace possesses in the sacred humanity of Christ, to open out, in a word, into that sacramental grace which, as we have seen, is a primary and fundamental element of the soul of the Church. It thus creates in those who have it a kind of living aspiration to that soul, a real and ontological desire for the Church. Men of this sort are of the Church, say the theologians, not yet re but already voto, mentaliter, by desire. Membership re and membership voto are here opposed, not as real membership to unreal, but as actual, consummated ontological membership to virtual, prefigured ontological membership, as membership in achieved act to membership in virtual act. Membership re, visible, corporeal, terminal, achieved, may be compared with membership voto, invisible, spiritual, prefigured, of desire; as the plant in flower is compared with the plant in bud; or, to take Bellarmine's comparison, as the man with the child still hidden in his mother's womb.

However reduced may be the activities of grace in such souls, they will still be in need of speculative and practical directives. They must know, for example—if they are to believe in them supernaturally—of the existence and providence of God, of the principles of morality and so on. Data of this sort are doubtless woven into the religious and cultural web within which they live, but are bound to be vitiated by endless errors. Each will have to do what he can on his own account, under the inner influence of the Holy Spirit who fails no one—though we may all too easily mistake our own voice for His—to sift the true from the false, the good from the bad. There will be omissions and inaccuracies, more or less serious according to the religious group concerned—Judaism for example or Islam being more helpful than paganism, itself a thing of many degrees. In so far as these religions shut out the truth they are instruments of darkness; but by such truths as they have retained (or perhaps regained), they may, however accidentally and imperfectly, be sources of light for millions of souls inwardly sustained by the Holy Spirit.

http://www.ewtn.com/library/THEOLOGY/chwordin1.htm#02

In the text of the Mystici Corporis, the Sovereign Pontiff clearly and authoritatively taught the requisites for actual membership in the Church. He issued as his own teaching the Bellarminian doctrine that “Actually only those are to be included as members of the Church who have not been so unfortunate as to separate themselves from the unity of the Body, or been excluded by legitimate authority for grave faults committed.” He likewise, however, spoke of the possibility of salvation for those who “are related to the Mystical Body by a certain unconscious yearning and desire (inscio quodam desiderio ac voto).” He depicted such individuals as existing in a state “in which they cannot be sure of their salvation” since “they still remain deprived of those many heavenly gifts and helps which can only be enjoyed in the Catholic Church.”