In Harry Potter, it seems like Time Turners are mostly used to correct minor things or do things that wouldn't have any major effect. Also, in Prisoner of Azkaban, it seems like Time-Turners/time travel is strictly "fated" or already predestined by history (time travel doesn't really change anything--rather, it ALLOWS what was already meant to occur to happen). This is shown when Harry and Hermione rescue Buckbeak and Sirius, and Harry saves his past self.
In time travel theory, this is called the Novikov Self-Consistency Principle, which states that "Nothing can be changed because anything a traveler does merely produces the circumstances they had noted before travelling".
Now, here's my question. In the book, it also states that wizards have accidentally killed their past or future selves while time travelling. But how is this possible under the Novikov Self-Consistency Principle?
Lastly, if someone were to die, does that mean that someone else could use the Time Turner to quickly stop that person from dying in the past?
EDIT: It's different than the question linked above because I never asked if going forward in time is possible in Harry Potter. I asked how is murdering past or future selves possible under the theory noted above, and how if it would be possible to go back in time to prevent someone from dying.