I'm going with a spin of the multiverse theory similar to what they explain in the EndGame movie: everytime she respawns she starts a new branch of the timeline form that point or her birth. Her individual timeline is effectively continuous which is how her "future" can still be read. When she "jumps" back to her birth, shes jumping to a new parallel existence forming that only deviates with her interaction (as a passive observer things play out exactly the same yadda yadda). In those regards no one ceases to exist ... they live a full life that isn't erased, its just isolated to that timeline. Heck you can argue shes creating life that would have never existed with her costant "timeline meddling" as she looks for the perfect future (hmm ... may have stumbled on the theme here ...)
"but that means its not the 616" ... meh. Her first life, her birth started in the 616, her mutant powers just means she exists beyond it, and the rules of the multiverse in every comic are wildly random anyway.