I can only speak for German law: When a car breaking a traffic law is identified (by number plate), the registered owner of the car gets sent a letter notifying them and ordering them to identify the driver.
If the owner can't or won't name the driver, the owner has to pay the fine. The law assumes that either you let someone drive the car, then you must know who it was, or at least be able to help the feds in their investigation. Or the car was stolen, but then it was on you to report the theft immediately.
It does get trickier when it's a criminal case, cause in Vaymo's case, it's difficult to determine who is personally responsible. This is where new laws are required. One possibility would be looking to the data privacy laws: Here, every affected company needs to appoint someone responsible for data privacy. In case of a violation that person is personally responsible and can be punished, including prison time, if they haven't done their due dilligence.

So for self-driving cars, every company would need to have a "traffic safety director" who is legally required to be in the loop for all decisions regarding traffic safety, has to report any legal violations to their superiors and the public, and is personally responsible for ongoing gross violations. (It's a very well-paying job.)