The issue here is necessity of good works alongside faith, and, of course, the necessity of prayer for the dead. Imputed righteousness vs infused righteousness is a theoretical debate, and not directly pertinent here. It is true that I know of no Protestant that says we should do bad works, so so long as the sin of presumption is avoided, good works are preached, and the dead are prayed for, we are on the same page, more or less.
However, once prayer for the dead is discarded, salvation of souls is very seriously at stake. The issue ceases to be theoretical.
From my vantage point, the discussion is all about imputation. I know that others disagree. (Otherwise we wouldn’t be having this discussion :>)
The bottom line, however, remains: have they or have they not persevered.
What are ways to persevere:
1. Have you sin not counted against you, so that you have a judicial righteousness and not a righteousness of your own.
2. Live a life with zero sin, so that no sin can be held against you.
3. Life a life which includes sin, but balance that sin by a more weighty portion of righteous acts that cancels out the sin.
4. Combinations of the above
As David says, “Ps 32:2 - Blessed is the man whose sin the Lord does not count against him and in whose spirit is no deceit.”
Prayer for the dead? You sound like a Mormon, LOL. When you’re dead, there’s no more need for prayer. The decisions you made concerning salvation were made before you die.