If time travel to your own past (rather than creating an extra time line) is possible hypothetical people with access to time travel who are determined to kill their grandfathers (before their parent's conception) have (in the sense of actions in inconsistent hypothetical time lines that influence which possible stable time line comes about) all eventually created a stable time loop where they don't exist as people who are determined to kill their grandfathers.

(e. g. they succeed and influence the time line in such a way that their other parent has a different child with someone else instead who goes back in time and accidentally kills the would be grandfather of the first person. Or they die in a freak accident that influences which children their would be grandfather has, which means a different grandchild that time travels with different actions and influences what grandchildren the grandfather ends up with until a grand child comes into existence who coincidentally influences the time line in just exactly the right way to bring their own existence about. Or something more complicated.)

Since I prefer to exist I will not time travel in any way that seems likely to make my existence inconsistent and take actions to make it consistent when it seems to be inconsistent without such actions. For example if I learned that my grandmother's fiancé was murdered by someone who claimed to be his grandchild and I had access to time travel I would try to stage that murder and take the fiancé back to the future with me.