I think, what happens if you die at mementos? It's supposed to be a cognitive world, so, people forgets you? Or you just die? So what's with that?
If everyone forgets you are you really alive?
Technically, yeah, but in the practice no, you are like a phantom I guess or you are there, people know that is someone there, but, doesn't know who's that person?
If you die in the cognitive world you just die, that simple, the only difference would be that people will never find your body
Well it makes sense, but, I don't think that fits well with is everyone's mind, cause you are not really risking your physical part, you're risking at the mind
You are confusing someone's cognitive self with their real self and the shadow self. If your real, physical self enters the place and die, you just die, nothing more, nothing less.
If it's your cognitive self, chances are that nothing will happen because that one is only the way someone or a collective group sees you as; only the cognitive self is gone when killed and it will change nothing in someone's mind.
If it's your shadow self the one that dies, then you die in the real world too. Whatever happens to the shadow self and whatever it is affected by... then it'll have a direct consequence with their real selve's mind
(This is all following P5's rules, none of this works the same exact way in previous titles.)
Other than that, there's what happens at end of the game but even that's a bit of an exception to the general rule.