Probably the same thing a new-to-the-area human would do if the sign was removed. Where I live there are many intersections where only 1 road has stop signs. I'd imagine there are other areas were the norm is a 4 way stop.
As for damaged, I would imagine it can still recognize the sign as often in image recognition you do not need the whole picture to confirm a match.
Either on the first video or some news, i think i heard the ability to drive where the lanes are not clearly defined. Things such as snow would absolutely requires such reconstruction.
IIRC it would automatically make a note of your location when you pass speed bumps or bad patches of road and adjust the suspension accordingly.