There's a ghetto way to fix that. Get a piece of tube similar to the size and strength of golf club tubing. Cut a couple of inches off and cut some teeth into it, you can put the tube in a drill chuck and drill around the screw, eventually you'll loosen enough that you can get the screw out. Then drill for a dowel, insert dowel with glue, allow to dry and you're golden.
I have a piece of tube in my toolbox that does this job because it's unavoidable with old screws.
There's a ghetto way to fix that. Get a piece of tube similar to the size and strength of golf club tubing. Cut a couple of inches off and cut some teeth into it, you can put the tube in a drill chuck and drill around the screw, eventually you'll loosen enough that you can get the screw out. Then drill for a dowel, insert dowel with glue, allow to dry and you're golden.
I have a piece of tube in my toolbox that does this job because it's unavoidable with old screws.