Does Hades (The bosom of Abraham) still exist after Christ's resurrection I've been listening to this pastor from AoC Network that has been talking about Hades as there is/was a place of torment and a place of peace, before Christ's resurrection. This is where people who God deemed as men of God or Godly men and women went before the resurrection of Jesus on the Cross. He says he believes (because the bible is not clear on this subject) that people who have died now days who have not had the opportunity to know enough about Jesus or know who he is, can make a decision to invite Jesus into their heart to be their savior, this is where they go. 

This sounds like the Catholic belief in Purgatory. 

I know the Bible isn't clear on the matter of "The Bosom of Abraham" in today's world, but I've been taught that "The Bosom of Abraham" was closed off when Jesus came back for his disciples after his death and brought them to heaven with Him.  Now, this pastor from AoC says he believes that the Hades that was called "The Bosom of Abraham" (which this pastor describes as a place of peace) still exists (but of course is not called "The Bosom of Abraham" because Abraham is up in heaven,) for those who have not heard of Jesus or had the opportunity to accept his free Gift of Salvation, i.e Babies who are unborn and those who die as infant babies who cannot know Jesus yet, because they cannot understand yet. 

My question is: "Does the side of Hades that was once "The Bosom of Abraham" still exist? Is this what the Catholic's call Purgatory, and where is this found in the Bible?"
I will answer the question from the viewpoint of Roman Catholic doctrine.

Before Christ's death, the state or "place" of the souls of all dead people (Hebrew sheol, Greek hades and Latin inferus [1]) was divided into several "compartments".


Gehenna or hell (latin infernus [1]), inhabited by the souls of the damned, where they are tormented by fire (Mt 5:22,29,30; Lk 16:23-24). It is de fide doctrine that this is an everlasting state for each soul in it, and consequently that, as a potential state for souls or "place", it existed before the death of Christ,  exists after it, and will exist forever [2].
The "Bosom of Abraham", "Limbo of the Patriarchs" or "Limbo of the Fathers" (Latin limbus patrum), inhabited by the souls of the purified righteous before Christ's death, where they did not suffer any torment, did not see God, but were comforted by the expectation that at some future time they would be redeemed and taken to the vision of God (Lk 16:22). It is de fide doctrine that this was a temporary state for each soul in it, which ended after Christ's death, and that, as a potential state for souls or "place", it existed only before the death of Christ [3].
The Limbo of Infants (Latin limbus infantium or limbus puerorum), inhabited by the souls of those who die in original sin only, where they do not suffer any torment, do not see God, and do not have any expectation of being redeemed and taken to the vision of God at some future time. It is de fide doctrine that this is an everlasting state for each soul in it, and consequently that, as a potential state for souls or "place", it existed before the death of Christ, exists after it, and will exist forever [2]. (But it is not de fide doctrine that there are actually any souls in it, because it is not de fide doctrine that any person actually dies in original sin only.)
Purgatory, inhabited by the souls of the righteous who still need purification, where they suffer a pufifying pain which is essentially different from the torment of gehenna. It is de fide doctrine that this is a temporary state for each soul in it, which ends when it is completely purified (after which the soul went to the "Bosom of Abraham" before the death of Christ and goes to the Beatific Vision after it), and that, as a potential state for souls or "place", it existed before the death of Christ, exists after it, and will cease to exist at the time of Christ's Second Coming and the resurrection of the dead.


Notes

[1] There are two different Latin terms, which must not be confused:


Inferus,  meaning just "low" (comparative: "īnferior"), refers to the global state or "place" of the souls of all dead people, encompassing all of the above "compartments". This is the term used in the Apostle's Creed or Symbol of the Apostles when it states that, after his death, Jesus "descendit ad inferos" (plural accusative of inferus) [1.a].
Infernus, a derivative word, refers to gehenna or hell [1.b].


[1.a] https://en.wiktionary.org/wiki/inferus

[1.b] https://en.wiktionary.org/wiki/infernus

[2] After the general resurrection of the dead, the whole human person, soul and body, will be forever in that state.

[3] Pope Benedict XII in his 1336 Apostolic Constitution "Benedictus Deus" [3.a] [3.b] defined that the souls of all the righteous who were completely purified at the time of Christ's death were taken to the Beatific Vision at that time, and that after that time, the souls of all the rigtheous, once they are completely purified, go directly to the Beatific Vision. From that, it follows that, after the death of Christ, the "Bosom of Abraham" no longer exists as a potential state for souls or "place".

[3.a] http://www.papalencyclicals.net/ben12/b12bdeus.htm

[3.b] http://www.ewtn.com/library/PAPALDOC/B12BDEUS.HTM