The first time it happened to a spare bedroom door, I had no idea what to do, and locked the door latch up in my desk drawer so noone would try to "fix" it wrong. Several months later I stumbled across a note in an issue of Old House Journal, with the advice to shove the wooden ends of matches covered with carpenter's glue into a stripped out screw hole, let it dry for 24 hours and then re-screw the screw into the now newly filled hole. Bingo! It works.
Here it is demonstrated--
Problem -- door latches, but without a working handle on the other side, can only be unlatched from this side:
Hardware removed, with two match sticks glued into the stripped hole: