Is this legal for a Vet to do?

My mother in law separated from my father in law a few years ago. She moved to an apartment that wouldn't allow her to take her 2 registered dogs with her. The dogs have resided with the father in law since then. Recently one of the dogs started having seizures. The father in law was unavailable at the time so his live in tenant took it upon herself to take the dog to the vet. The vet pointed out that this tenants name wasn't on the dogs papers; but being a friend of hers, she went ahead and prescribed medication for the animal. A few days later the dog had a seizure and went into a coma. The tenant tried one time to contact the father in law. When no one answered the phone she decided to take the dog to the vet and promptly have it put to sleep. Only my mother in laws name is on the dogs papers, so did the tenant have the right to put the dog to sleep? And what about the vet? Did she break the law by killing the dog without the owners consent?