How to fix stripped screw holes in drywall? (Without using drywall anchors)
Drywall without anchors has very little holding power. There really isn't a method to repair stripped holes in it either. You could insert a toothpick in the hole and hold it in place while you screw in the screw and the screw would hold but not with any power. You could also use a larger screw which would cut into new drywall. None of these will give you any holding power. Using an anchor of some sort is your best bet so you don't have to go through this again.