Quote from dmo:
Let's say you offer a call at 1.00, and Joe Blow buys it. Your contract now is not with Joe, it is with the Options Clearing Corporation. Joe's contract is also with the Options Clearing Corporation. So if you go bankrupt and can't meet your obligation to sell Joe stock at the strike price, Joe's option is still good. That's the function of the OCC - to guarantee every trade by standing between the two parties and assuming the obligation for that option to perform.
If at some point Joe decides to exercise his option, the OCC will assign it to somebody who is short that option, but not necessarily to you.