Looper did that. He killed himself to stop his future self kills others, but by killing himself he stops his future self to go back in time to kill others, but if he never goes back in time he has no reason to kill himself in the first place.
Looper bypasses the grandfather paradox by using self-correcting timeline. Any change done to the present by future entities would still affect the future, including the entities who present now themselves, but the change that happened to the future (including future entities that present now) would not change things that already happened now. So if someone from the future goes back in time to kill their grandfather, the future person would be erased the moment they killed him (or the moment they change the past so that their future existent is no longer possible), but the said grandfather would still be dead. So in this example, any witness would see someone walking up to a guy shooting him in the head and suddenly vanish, and the victim would be on the ground dead.
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