I own a 12 gauge F extractor gun #25179. The extractor will fall out the barrels with the gun disassembled but not with the barrels on the receiver. The breech face prevents the extractor from falling out when assembled. The extractor looks just like yours.

I have learned to take the extractor out when cleaning the gun and then simply replace it.

Buck Hamlin offered to put a retaining screw in for me but I decided not to bother. Just have to pay attention and wonder why Uncle Dan laid this extra chore on me!