How do you know that reality does not collapse immediately? At any given instant you could be a fresh brain that just came into existence, all your previous memories which imply a life lived up to this point also formed in that same instant.
Indeed the bigger issue as I see it is that the only "sensible reality" that can exist is the one you subjectively experience. Since that one is the only sensible one, it's the only one you perceptually would be able to hang around for - even if it's actually a conincidental series of flickers of sapience across trillions and trillions of years.
i.e. a time stepped simulation, absent external reference, doesn't know how long it's been between the actual steps - could be seconds, could be hours, could be years.
EDIT: Like the real issue with "death" is that it's not "eons on darkness" - which is why I think people get afraid of it (or one of the reasons) - but that actual, literal non-existence is inconceivable even though we all did it - 13 billion years of not-existing in the universe, then suddenly you.
So after you die the same problem re-emerges: the conscious experience of "you" ends...but then from the subjective blink of an eye if something happens to restart that information process just right, suddenly again, you - and it has to be you, and no one else, because if it wasn't then well, it would be someone else - i.e. why am I me, and not my wife or son for example?
What if it was someone who just happened to be extremely similar to you? There's a decent probability that someone extremely similar to you will come into existence during the finite lifespan of the universe. Would that person be likely to be "you"? By comparison, would they be more "you" than a version of yourself that woke up with brain damage?
> and reality does not collapse immediately
How do you know that reality does not collapse immediately? At any given instant you could be a fresh brain that just came into existence, all your previous memories which imply a life lived up to this point also formed in that same instant.