Thanks for the question.
Purgatory will no longer exist after the end of time. Those who are alive
at the Lord's Coming will be perfected and purified at that time. Remember,
on the last day, the dead shall rise. All souls will receive resurrected
bodies. The damn will receive eternal punishment in the flesh. Purgatory
is meant to purify the soul. Once we receive our resurrected bodies, they
will need completely purified souls so purgatory ends with the Resurrection
of the body.
It's important not to get caught up in the various paradigms used
to explain purgatory. The actual doctrine as found in the Catechism is
- There is purification after death for those who have not
been fully sanctified in this life.
- This purification involves pain.
- The living can pray for the souls being purified and those souls
can pray for the living.
- Souls being purified are destined for heaven.
Any attempts to define
purgatory in terms of time and space are simply attempts to grasp a Mystery
beyond our comprehension. They are theological opinions and paradigms that
provide us with a "relative" understanding.
We live inside time and space, so we think in terms in time and space,
but time and space could be metaphors for intensity.
Purification after physical death is simply the completion of the work
of Christ started in us on earth. As St. Paul wrote to the Philippians:
who began a good work in you, will be faithful to complete it until the
day of Christ Jesus.” (Philippians 1:6)
If you really need paradigm to relate to,
you could say that, as the last day grows near, God increases the intensity
of the purification process on earth or in the after life, but again,
that's just a metaphor. For all we know, purgatory is a momentary condition
for everyone. Nevertheless, the prayers of those living in the future
are made efficacious for those who died centuries ago. Remember, God stands
outside of time and makes the past, present to us, and our present, present
to those in the past. For example, your great grandmother might have died
in 1935 and "could" have been purified instantaneously due to
your prayers in 2009 for her soul. Your prayers would have been applied
to her purification.
Finally, it's important to understand the nature of the pain suffered in
purgatory. The pains of hell are punishment for rejecting mercy. The pains
of purification are healing pains. Yes, they've been described as "temporal
punishment", but even temporal punishment is for the benefit of the
person being "punished".
The "temporal punishment" juridical
metaphor is one of several metaphors that can be used to explain the process.
Purgatory could just as easily be explained as a Holy Ghost Hospital, where
patients suffer healing pain. Yes, the pain is real, it is a source of
torment, but at the same time it is a source of joy, because the person
realizes they are getting better.
I hope this helps,