This type of time paradox is usually resolved through a method of branches in time.
This line of thinking holds that just as every possibility creates a branching in reality (slow down at the yellow light, or speed up?), so a time-travel caused breakage would also cause two different paths, though one might, in a subtle way, end/loop a bit further up the line.
Thus one branch where the person lives, but travels back in time, and the other branch, where the person died a week ago...