Well, considering that the event of your atoms suddenly appearing in your relative past alters the universe, your old future probably wouldn't exist, though an indistinguishably similar one might. Considering that your appearance is a single event, and that it alone will change the future, then nothing will happen to you if you prevent your own birth, since you already became a part of what used to be your past.
As long as someone uses time travel to visit the past, the universe would iterate through countless variations, until it created a stable time loop, at which point it would continue until the next time traveller, again iterate, repeat.
At some point, time travel becomes completely impossible, and then the universe would proceed purely linearly.
However, if one time traveler interrupts what had already settled into a stable time loop, the result would likely recursively iterate until it reaches a state where both time loops are stable.
This is all based on the viewpoint of the universe as a purely linear series of events, and reverse time travel would be viewed as copying the exact state of a past moment on the hypothetical timeline, inserting the time traveler, appending it to the end of the timeline, and continuing from there, unless the state resulting from the insertion of the time traveler has already occurred, with absolutely everything matching perfectly, right down to the quantum level, and perhaps beyond.