Some ideas are:
- You branch off into another timeline and your actions make no difference to the previous timeline
- You’ve already taken said actions but just didn’t know about it so nothing changes
- Actions taken can have an effect (so you could suddenly erase yourself if you killed your parents)
- Only “nexus” or fixed events really matter, the timeline will sort itself out for minor changes
- something else entirely
You may like the show Dark, if you haven’t already seen it.
Dark
The season 3 story was pretty much why I’m interested in this trope! Although I maintain Dark was not a stable time loop story, it just had the appearance of one.