Continuity mistake: When the T-1000 walks past the deactivated T-800 just after being shot at by Kyle Reese, you can see that the T-800 has taken a lot of damage to the face and the nose is missing. Once the T-800 gets up after being reactivated you can see that the nose is back with a lot less damage to the face with a close up shot.
Chosen answer: If we accept the theory that alternate timelines even exist, branching off every time there is deliberate interference through time travel, then it becomes entirely possible for time travelers to continue existing in alternate timelines, even if they erased their own origins.
Charles Austin Miller