But all of those cars are insured (and that insurance is underwritten) today. So the liability already lives on the balance sheet of insurance companies. Maybe the specific companies change...
eh, right now most people are massively underinsured; minimum coverage in California is like $35k, and most insurance companies won't sell you a plan with more than a half million of liability (at least not without an umbrella policy) - if we stop subsidizing driving through pushing costs on to victims of accidents, the cost of driving will go up. But yeah, it should be about the cost of a good umbrella policy+auto policy is now, modulo any savings if the self-driving car gets in fewer accidents.
but note, we're paying most of that already in the form of people who are killed and under-compensated by under-insured drivers. Increasing liability insurance minimums would roll that cost that is currently born entirely by the victim into the cost of operating a car, which is where it ought to be.