I can see bearings failing, belts getting old and other things that wear getting worn out and breaking, but how would a stud just fail? The load on it should never be getting anywhere close to its strength limit. Metal doesn't just get old and break for no reason, usually something causes it to break.
Are you sure that something didn't seize up or otherwise prevent that belt from turning smoothly? Was there any warning shortly beforehand that something was about to happen?