A friend of mine bought a horse from someone who claimed ownership of the horse because the original owner hadn’t paid board and training. The original owner sued, and my friend had to surrender the horse. If the seller didn’t acquire the horse legally, the BOS doesn’t mean anything.
I can imagine there would nothing more frustrating than taking a project horse, finishing it out and even showing it, and then having it taken away because you found out you didn’t actually own it. Following this line of thought, let’s say the horse got great, you start advertising/showing, and the original owner (or family) sees the horse and comes out of the woodwork. Paper trail for sure if you do it!