I would expect your friend to pay the $500. After all, you were doing your friend a favor in caring for the dog, which made you a bailee for no personal gain. Since the bailment was to the primary benefit of the bailor (your friend), the bailee (you) must be found grossly negligent to be liable for damage done to the bailment. You were not negligent at all and actually acted to mitigate the damage done to the dog, keeping it from dying or losing use of its leg. You went beyond ordinary care by taking the dog to the emergency vet. Also, it was the dog that caused his own injury, not you. Finally, if the dog's owner is as you indicated, a close friend, there is no way they would or could allow you to pay. Rather, I would expect them to be indebted to you for taking the extra time and effort to obtain care for their injured pet, I know that I would.
Several years ago, on a dark rainy Christmas Eve night, a car hit a basset hound across the street. The poor animal was howling in pain and would not allow anyone to get close to it. I fashioned a rope loop on a pole and took a blanket with me and caught the animal, wrapped it in the blanket to avoid being bitten, and carried the 80 pound dog to our car and Karen and I drove downtown to the emergency vet. The vet examined the dog and told us it was seriously injured and he could either put it to sleep or operate, which cost he estimated at $700. Without even asking the other, we both said "operate”, which we would pay if the owner could not be found. The next morning I was putting a large sign in the front yard indicating we had found a basset, when a car with a young couple pulled in and identified them as looking for a basset. They had just driven back on Christmas day from visiting relatives in Virginia because the person who was caring for their TWO bassets had called and told them one of the dogs ran out of the house when they went to feed them. The owners went to the emergency vet and took care of the bill. We thought no more of it until around St. Patrick’s Day we got a letter from THE DOG, thanking us for saving her life! Said letter was signed with a paw print and included pictures of the recovered basset with her sister basset, both on their own loveseat. Also included was a gift certificate for two at a local steakhouse.
Yeah, I’m betting your friend will not stand for you bearing the expense of their dog.
