Per current teaching in the Catechism, each person earns a particular judgment:
CCC 1022 Each man receives his eternal retribution in his immortal soul at the very moment of his death, in a particular judgment that refers his life to Christ: either entrance into the blessedness of heaven-through a purification or immediately, or immediate and everlasting damnation.
As posted here, the non doctrinal term "second judgment" looks like it addresses those who have not yet received particular judgment in the last days.
(Catholic Answers) At the end of time, when Jesus returns, there will come the general judgment to which the Bible refers, for example, in Matthew 25:31-32: "When the Son of man comes in his glory, and all the angels with him, then he will sit on his glorious throne. Before him will be gathered all the nations, and he will separate them one from another as a shepherd separates the sheep from the goats." In this general judgment all our sins will be publicly revealed (Luke 12:2–5).
For those who have been purified, they are in sufficient state of grace to be included in those who are "with God" rather than those who are not.
III. The Final Purification, or Purgatory
1030 All who die in God's grace and friendship, but still imperfectly purified, are indeed assured of their eternal salvation; but after death they undergo purification, so as to achieve the holiness necessary to enter the joy of heaven.
1031 The Church gives the name Purgatory to this final purification of
the elect, which is entirely different from the punishment of the
damned. The Church formulated her doctrine of faith on Purgatory
especially at the Councils of Florence and Trent. The tradition of the
Church, by reference to certain texts of Scripture, speaks of a
cleansing fire
Note: As I read the text, the Council of Trent revised a previously held dogma from Benedict XII (ca. 1336, Benedictus Deus) on the impact of dying with the stain of mortal sin on one's soul.
With the above considered, it is pretty difficult to get into hell in that it requires a complete unwillingness to "turn towards God" at all. (Repentance has a meaning from the original term in Hebrew that we could read as "turn toward" or "turn again" with a positive connotation).
1037 God predestines no one to go to hell; for this, a willful turning away from God (a mortal sin) is necessary, and persistence in it until the end.
This indicates that not only is mortal sin a requirement to be consigned to Hell, but also the stubborn refusal to repent/atone for said mortal sin has to be maintained. That state looks to be a criterion used during particular judgment.
