Yes, there are narrow exceptions under California law.  The following circumstances could be used by a dog owner to escape legal liability (fault) if:

  1. The dog bite victim was a trespasser, and it was not a foreseeable trespasser (meaning the dog owner had no reason to expect the potential trespass in the past for example);
  2. The dog bite victim was a veterinarian doctor who was treating the dog medically at the time of the incident or dog bite;
  3. The dog bite victim was committing a felony;
  4. The dog bite victim provoked the dog; (also known as "contributory negligence")
  5. The dog who bit or attacked another was assisting the police or the military at the time of the incident/attack or dog bite.

There is a possibility for the dog bite victim to enact or direct a legal claim to other (or against) possible defendants, including employers, landlords and dog breeders. It is even possible to make a claim against someone who negligently entrusted a dog to another person who could not control it, like a child. Claims against people other than the owner might be crucial under certain circumstances, such as when the dog owner lacks insurance.  However, to obtain legal liability of any other party you generally have to prove that the other party knew of the dangerous propensities of the dog, and where the dog was located (like for landlord dog bite negligence for instance).