With one linear timeline, you basically have Back to the Future rules. You can go back and change things, even if it rewrites you out of existence. Of course, there are some logical paradoxes that arise from that theory of time, so most versions rely on some delayed repair mechanism, like how the photo of Marty slowly disappears, or how The Ancient One explains the Time Stone to Professor Hulk. Time Cop, Butterfly Effect, and Looper do the same, with changes going into immediate effect like old injuries becoming later scars in real time, but erasing yourself really ought to be devastating to spacetime itself. I liked the concept in Butterfly Effect where the time traveler experiences all the memories of their new life in the altered timeline with every new change, but then they abandon the hard sci-fi aspect to get cute with stigmata. Donnie Darko probably handles it the best, where time travel itself creates a universe-ending paradox that requires the destruction of the time traveler.

Essentially, you jump from now back to another location in spacetime where you didn’t exist the first time around. If you overlap with yourself, you’re either going to gain a new retroactive memory, or there’s some magical maguffin that erased the memory (like the Tardis does for the Doctor), or some universal force reconciles the timestream and eliminates the paradox.