These screws and nuts are for the case clasps and latches on the vintage Singer Featherweight case.
The nuts on the backside of the screws will suck into the wood but whatever is left of the screw beyond the nut will need cut off (hack saw, Dremel, etc.). Sometimes you can peel back the fabric that is on the interior of the case and reglue it, otherwise you can glue a piece of black fabric back over the nuts to protect the machine.