My dinette light fixture fell down

All of these are helpful. The problem is the screw actually bites into something I cannot see. The dinette ceiling is a layer of something like reinforced foam board. And then the screw passes into something presumably a wooden slat where the stripping might have happened. But none of that is visible.

The Teflon tape didn't work. It's a little uncomfortable enlarging and drilling into something I cannot see. An alternative would be a shorter screw, with an anchor installed in the ceiling itself.