I've had to deal with stripped screws in wood a couple of times on my RV. But I'm not sure you can trust them anymore no matter what.
I use Gorilla Glue. It is a glue that expands on contact with moisture. First I take a syringe and squirt water into the hole. Then I squirt in the Gorilla Glue. I push the nozzle up to the hole and squeeze like crazy to inject as much glue as possible. Then I screw in the screw as "tight" as it can get, assuming there is anything left to bite into. The glue will expand and squirt out if possible, and it is a bear to remove so if it starts squirting out I would clean it up immediately. Sometimes you can use a razor to remove the hardened expanded glue foam if you are careful. You might consider wiping the surrounding area with a thin coat of petroleum jelly to prevent the expanding glue from sticking if it is going to be in a place of concern.
The expanding glue tends to get squirted into all the remnants of the wood around the screw.
Steve