Being "Erased" and Anomalies

Time Travelers who don't protect their identities find themselves at the mercy of assassins who would gladly remove those who would stand in their way. This could be done by two means. Killing a younger version of their foe or an ancestor to prevent their births. This is referred to as "erasing" someone from the timeline. Of course there are exceptions. Those that for some reason or another (usually due to something paradoxical in nature) continue to exist despite having no logical reason for still living. These anomalies might be created through a shift in events, diverged timelines, or other unusual temporal disturbance that affects the being.