What we have here is a paradox. Jack enters the time crack and is killed as a result of going in there, but wait... he's not killed because he didn't exist, because we went into the crack, but he did exist before he went into the crack. I think it's a paradox that even Jack can beat. I think what would happen would be he would forget everything about himself like some sort of "human vegetable" until he'd had time to "heal" himself.