I work at a boarding stable that had this happen once.
The man who owned the horse was rich and from the city, and basically whenever he happened to be in the area he came and ran crap out of the horse down our entire 5 mile trail. This happened maybe twice a year.
Eventually it got to the point where the man moved across the country, and pretty much forgot about him. The BO kept trying to get hold of him to ask for money, and she kept billing him. The horse was at the barn for over a year without payments made, so she finally called the owner up and got a hold of him one day and basically said either you pay everything now, or that horse and all his tack is mine. He said keep the horse, and he'd send his papers etc. She never got his papers.
He is now one of our lesson horses.