When it comes to memories, it tends to vary. "Wild" Digimon that die of old age lose all their memories, while human-trained Digimon that die of old age retain all of them. Digimon that die unnaturally, such as in combat, tend to lose at least a part of their memories, but may lose all of them or retain the majority of them, depending on various factors (the individual Digimon, the way they die, the situation in which they die, etc).

Incredibly powerful Digimon like the Demon Gods, Seraphimon, and the like retain the majority to all of their memories when passing, even if they were killed unnaturally (as they're unlikely to die naturally of old age, at least not within even a few lifetimes). However, they are vulnerable to possibly having their memories wiped if killed in an extreme or traumatizing battle.