LEGAL RECOVERY: How can you know if the person who owned the dog that bit another has a valid liability insurance policy to cover for all the damages?

You can speak with the dog owner and see if he has any homeowner's or renter's liability insurance.

However, you have to be careful here.  Some people deny they have a liability insurance policy when in fact they do have it. Therefore, you should not solely rely on the dog owner's statement that he or she does not have a liability insurance policy.  You should contact a California dog bite lawyer for this; for example, I can hire a company to research and find out about any insurance policies and how to best navigate a dog bite claim when insurance is difficult to find.