It's hard to say. That's not really how it works where I'm from... although I guess it did, in fact, happen once but that's a really complicated story that I technically wasn't around for.

But one scenario is that the timeline keeps going on, but you no longer exist in it. Maybe everyone's memories of you gets wiped or it's like you vanished. Another is that maybe that timeline just stops being a thing altogether.

[ the only time something like this happened with karkat, the timeline had gotten completely screwed over anyway and had to be completely retconned. thus, he does not remember it happening. ]