Yes, the autonomous car will need to make a judgement whether to “limp” out of a situation it is unsure of, or whether to stay where it is. It’s weighing two risks against each other). This happens whether it’s 95 or 99.99% autonomous - it just happens with different frequency.

It could also be possible for the occupants of the car (if it has any!) to pick up a smartphone and guide the car to safety if needed. Part of the attraction of autonomous vehicles is that if can operate without occupants, however.

I had to drive once on a punctured tire that was deflating. No shoulders due to construction, and in fact I had to speed through the work zone to make sure I got to an exit while I still had some air.

The real world is a very very messy place.