I buy the option at strike 100 from you, and hedge it. Underlying goes up, I sell some, it then goes down, I buy some, I've enough made money on the hedge to cover your premium. Price goes back to 100.

You did nothing in the meantime, so you collected the premium on the expired option.

Note this system isn't closed, we have not accounted for where the money came from. The market makers in the underlying are out the amount of the hedge gains.