When your order fills, the trade is immediately novated: the OCC becomes the buyer to every seller and the seller to every buyer. You never have counterparty risk to the person on the other side, only to the clearing house and your broker.
The OCC also sets adjusted-option terms after a corporate-action, runs exercise-by-exception, and allocates assignments to clearing members, who then allocate to accounts.
Example: you sell one XYZ $50 call to an anonymous buyer. You do not owe that buyer anything — you owe the OCC. If they default, you are unaffected. If you default, your broker covers it and comes after your account, not the buyer's.
Related: clearing-member, assignment-allocation, adjusted-option, exercise-by-exception