Legal Question in Personal Injury in California

No, unless that stray dog has been on your property for a considerable time and you failed to call the pound to remove said dog. Unless you owe some duty, you are not liable for this stray dog.

Only if a judge finds you liable, but I think it's far fetched.

You would not be liable because a stray dog was seen on your property. You did mention if the dog bite occurred on your property. I guess a creative attorney could argue that the dog was not truly a stray, but was your dog. Arguing something like the dog spent a majority of its time on your property, you fed the dog on a regular basis, and you acted in other ways that showed the dog was under your care and control for a reasonable amount of time. It would probably be a long shot if the dog was truly a stray.