Alternatively - pump some sort of 'No More Nails' type filler into the space to fill it completely.
Leave it for , say, two weeks - don't follow the 24 / 48 hour or whatever hour guidance on the pack.
Really need to let all the water / solvent get out of it - should be hard as the wood by then.
Then cut away any excess with a craft knife.
It'll then take screws and let them cut new threads (suggest to drill pilot hole before screwing).