What does the Catholic Church teach about Purgatory?
A place of purification
Purgatory is an intermediate state after physical death in which some of those ultimately destined for heaven must first “undergo purification, so as to achieve the holiness necessary to enter the joy of heaven,” holding that “certain offenses can be forgiven in this age, but certain others in the age to come.”
And that entrance into Heaven requires the “remission before God of the temporal punishment due to sins whose guilt has already been forgiven,” for which indulgences may be given which remove “either part or all of the temporal punishment due to sin,” such as an “unhealthy attachment” to sin.
Only those who die in the state of grace but have not yet fulfilled the temporal punishment due to their sin can be in purgatory, and therefore, no one in purgatory will remain forever in that state nor go to hell.