[Notwithstanding]

If one is dovirced and marries another, the sin of adultery exists until there is a declaration that the first marriage never existed as a sacramental marriage (anullment - rather different than a divorce in theory).

If the new "spouse" dies or the first spouse (the true spouse) dies, then the condition of sinfulness ends because the adultery no longer exists. But the person must repent and receive sacramental absolution.

[Notwithstanding]

Assuming the couple chooses to be in good stadning witht eh Church:

If the first spouse dies, the second marriage would need to be sacramentalized in some way (marriage vows officiated by a priest) because it is an adulterous cohabitation until the Church recognizes its sacramental nature.