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!”

But it’s ok because you don’t realize you’re stuck