It looks as though the nut has 2 flat sides to it and I'm guessing the plastic around it is stripped ot so it just spins. Try and you a small pair of needle nose pliers or tweezers even, on the flat sides of the nut.
One end angles the edges of the hole. The other end digs into the hole you drill and helps you turn it. It turns the opposite way of a normal screw. Could maybe use something like that and a screw driver to hold the other side.
This will also DESTROY whatever you use it on. Not the best way to unscrew something, but it might work as a last resort.
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