The car companies have enjoyed brand loyalty and the ability to sell feature bundles because many people associate their car with their identity. When you say “Mustang owner”, “Subaru driver”, etc. specific images come to mind, and across all cars you see things like people paying considerably more to e.g. have a fuel-inefficient engine because there are a few times where they can step on the gas and enjoy the rapid acceleration. Manufacturers made billions selling SUVs to people who thought safer, cheaper minivans were too boring.
That doesn't completely go away with self-driving cars – someone with 4 kids will still have different needs than the avid bicyclist or single urbanite — but a lot of it will become less important if people start thinking about their car as, say, the place where they play games or catch up on Netflix while they head home from work. Why pay Ford for the premium sport package when you can put the money into a faster mobile data plan or a better tablet? They certainly don't go out of business in that scenario but the business becomes tighter and less exciting if it becomes more of a commodity where people generally just buy whatever's cheaper.
The fact that the cars drive themselves really changes nothing. Car pooling reduces the total number of cars necessary. Public transportation reduces the total number of cars necessary. You might try to argue that car pooling will increase as a result of the change, but I don't think that is a given. You'd need to explain away surge pricing to convince me otherwise.
But certainly, if you'd like to sell me your Tesla shares now at half price and get to safety, I'll be a friend and take them off your hands for you :)