This may sound a bit unconventional and assuming that it is a recessed screw, I would get the proper sized screwdriver and glue it to the screw using either epoxy or Gorilla glue. Use just enough for the screw slot(s) and not enough to spill over and glue in the screw to the case. Hopefully, you will achieve enough grip to gently remove the screw.
Another possibility is to use a sharpened, flat blade jeweler's screwdriver to insert between the screw and the case so that you may pry upward as you remove the screw. Otherwise, you are screwed. (Sorry, I couldn't resist.)