Whether an organism leaves a corpse or not, and whether its corpse exists or not, if that organism dies at time t and does not regain life then it is dead after t.
Why not solve the problem by saying that upon dying an organism leaves a corpse, and it is the corpse that is in the state of being dead? There are several problems with this suggestion. Some organisms do not leave corpses. What corpses are left eventually disintegrate. Whether an organism leaves a corpse or not, and whether its corpse exists or not, if that organism dies at time t and does not regain life then it is dead after t.