Will owner of the car be liable if car was stolen then involved in a car accident?

No, unless someone can prove that the key situation was negligent.

It could be argued that the owner was responsible, because he negligently left the keys in the car.

No; the owner is not liable for anyone else driving the car, whether they have permission to drive it or not. The only way the owner could be liable is if he or she lets an incompetent driver drive. Good luck.

Generally you are not responsible for the unforeseeable criminal acts of others; however, if your negligence was a proximate cause of an injury producing situation, you could have liability. Certainly the lawyer for any innocent injured parties would more than likely sue the owner and the driver of the vehicle that caused the crash. The court would have to sort out the facts to determine if you had legal liability. Your insurer may not want to provide a defense to the claims as the vehicle was stolen, but they would owe you a defense on any claims of your negligence (even if they may not owe a defense to any defendants who acted criminally). Certainly you would need to read your insurance policy, and if sued, turn the papers over to your insurer. You may need to retain personal counsel if the attorney your insurer provided made any claims about non-coverage, reservations of rights, declaratory actions re: coverage applicability, etc.

Leaving the keys inside the car seems to be negligence so the car owner would be liable for up to $15,000 in damages if the accident occurred in California, but there liability insurance carrier might deny coverage because they negligently allowed someone eels to drive the car.

Not in Michigan.

If the car was deliberately left in a high crime area with the keys in the ignition and the doors unlocked and with the hope that it would be stolen, that might well be considered negligent conduct, but wouldn't necessarily lead to a finding of liability. On the other hand, if you live in a safe neighborhood and all the neighbors routinely leave their keys in their cars, and your car was parked up close to your house, an ultimate finding of liability would be much more unlikely.

As a general rule, the owner of a vehicle is not liable when that vehicle is stolen and then causes an accident. A rare exception may be made if the owner was grossly negligent by leaving the car parked, with the engine running, perhaps for an unreasonably long amount of time and/or doing so repetitively. Again, as a rule, the owner is not liable in stolen car accident cases.