My mare was $12k and was bought on a payment plan. We paid $6k upfront then an additional $1k until paid off. The buyer had our numbers, address, email, everything. I bought her while at a barn where they were friends with the trainers but I soon moved home. The mare came with me, but she knew the new location and we never missed a check.
Buyer held papers and I was made to keep her insured, which i still do. People were shocked she let us take the mare off the property but by that time we had proven our honesty. I never missed a text, I always updated her and she always got pictures. Once bought I now never speak with her. But I can imagine this is incredibly rare.
We also drew up a very cut throat contract. The only thing we didn’t add was the mare needed to stay on the property until paid off (which I’m grateful for because me and the trainers had a falling out).
It also doesn’t mean the person can’t care for the horse. I’ve never held back money from my mare. She gets all the chiro/massaging/shoeing that she needs and then gets the supplements, treats, injections anything that’s a necessity as well (and to her treats are indeed a necessity😂).
So TL;DR: it can happen but it’s not usual and a contract should be drawn up that both parties sign and have a copy of.