Sometimes I still marvel about how in most time-travel stories nobody thinks of this. I guess it really is true that only people who are sensitized to 'thinking about existential risk' even notice when a world ends, or when billions of people are extinguished and replaced by slightly different versions of themselves. But then almost nobody will notice that sort of thing inside their fiction if the characters all act like it's okay.)

The only story I've seen directly address this issue at all is Homestuck, in which any timeline that splits off from the 'alpha' timeline is 'doomed' and ceases to exist once it diverges too far from the alpha. The three characters with time traveling capabilities are someone who is extremely careful to avoid creating doomed timelines, one who is nihilistically apathetic about death and creates doomed timelines willy-nilly, and one who is a psychopathic monster bent on using his powers for destruction. Several times, main characters are shown experiencing existential despair over the idea that their own timeline might be a doomed one, and at one point a character with time-traveling capabilities realizes that the only way to prevent the destruction of the universe is to travel back in time, leaving his current timeline doomed. His realization of the implications of dooming that timeline and his efforts to somehow save his timeline's version of his only surviving friend were particularly poignant (to me, at least).