By law in the US the car manufacturer must warranty everything related to the emissions for I think it's 7 years. And CA extends that to 10 years if I remember correctly. So one way or another VW is on the hook to remedy the problem, either by bringing the cars into compliance or buying them back. And that's before any EPA fines which I read can be as much as $37k per vehicle.
If VW were a US company, they would likely declare bankruptcy as a way to start shedding their liability over this. I don't know how the laws work in Germany, and I don't know whether is a separate VW North America corp that might be left holding the bag. I'm sure there are armies of lawyers looking at how to best quarantine the damage. This is clearly company-destroying magnitude stuff, but I honestly don't think it's in anyone's interest for VW to get destroyed. All benefit the most by figuring out how to solve the problem.
Speaking of the problem, I owned one of these cars a few years ago. Loved it, but that's neither here nor there regarding the problem. It was mentioned that unlike pretty much everyone else who uses the urea fluid (is that what it's called, or is that piss?), VW used some proprietary incineration method to get ride of the NOx, but only on the 2L engines. I think the $64,000 question here is whether this device simply needs to be turned back on under normal driving conditions and the problem is solved, though with reduced performance? Or if their proprietary device is actually not capable of meeting the full spectrum emissions requirements, in which case this is a much harder problem to solve. Since everyone else, including VW in their 3L engines, is using DEF to meet emissions requirements, I suspect the VW proprietary approach actually doesn't work under all conditions and that's what lead them into cheating in the first place.