Is Purgatory a "second chance"?
Defined dogma
No. Purgatory is not an opportunity for repentance after death. Those who enter Purgatory have already died in the state of grace — they are saved. They will certainly reach Heaven. The soul's fundamental choice for or against God is made in this life and is irrevocable at the moment of death. Purgatory is the purification of those who are already saved but not yet perfectly clean.
Private revelation What the saints and mystics add
What the soul meets at death: the tribunal, the self-judgement, the anticipated judgement.
Accounts that bear on this