Assuming nobody else is immune and has the power to restart it. If someone else did have the power to restart time, I think the thought process would go:
Bob: "Aha! I have the power to stop time with the snap of my fingers"
[starts to snap]
Bob: "Oh wait! What if I'm not immune!"
[time is frozen]
Some dude elsewhere: "Weird, time stopped again! I guess I'll take advantage and rob this bank." Then, later "Ok, got all the money, now I'll just crack my knuckles to restart time."
[time is unfrozen]
Bob: "Wait... I just snapped my fingers and time didn't stop! I guess I don't have that power at all!"
That is an amazing story idea! One person has the ability to stop time, someone else somewhere has the ability to start it. They could even have a cat and mouse thing similar to Death Note...
Yeah, I actually think about this. People recognize that time is a dimension of our reality, but ask: why does it only move forward? But wat if it doesn't? What if we go backwards and forwards often? But our memories are "unmade" when moving backwards and "remade" when moving forwards. We simply can only perceive the forward direction.