I have on several occasions broken screw heads in pieces where I can't readily access or cut into the joint they're securing. Is there such a thing as a tiny core drill bit for cutting around what's left of the fastener so I can remove the rest of the wood piece it was securing?
Or is there any other technique for dealing with this situation when I can't cut the wood piece loose from behind using a reciprocating saw and can't just tear the piece free?