Odds are that stud is in there loose. Try a very short pencil with an eraser. Push the eraser against it hard and unscrew it. It might come out.
If not, "lightly" tap on the stud with a punch & hammer and then retry.
If no luck, try a good adhesive like JB Weld. Glue an allen wrench on it. After the glue has cured well, spray some PB Blaster (a penetrating oil) then carefully unscrew it. Any movement is good. Just work it left/right/left/right.
If all is hopeless, find someone skilled in detailed welding. He/she might be able to tack weld a bolt to that left-over piece. Then you have something to put a wrench on.
