I don't actually think it's that simple to 'repo' and sell a boarder's horse - I think the barn owner has to go through some bureaucracy and that there would be a paper trail, but as I don't recall the details, I'll look it up.
But I do know one thing - that in the US, the laws on that are at the state and local level. So it depends on your state and local laws, whether a barn owner is allowed to do that or not, and exactly how he does it. So it depends on where you are.
In general, barn owner/managers don't do this until the situation has become really desperate - the horse owner has disappeared and abandoned the animal for months, or simply refuses to pay.
Nor would I simply assume the barn owner was 'mean'. We always have to remember that the horse business runs on one main fuel - gossip, and what you hear about a barn owner may not necessarily be true - at all.
This is just one of the many things, though, that makes it all the more important to have a written boarding contract that both owner and barn manager/owner sign - and stick to. The typical arrangement, 'we do this this and this', 'okay, I'll move my horse here', it just really doesn't work out very well when a problem pops up.
And also, just another one of those things that point out that no one should get a horse if they aren't absolutely sure they can keep on paying board, on time, very consistently.
The right to sell a horse for unpaid board is usually called a 'stablekeeper's lein', and at least in Texas, it doesn't include tack and equipment - only the horse. It's found under the Texas Property Code law. And in Texas, the horse cannot be sold privately - it must be sold at public auction. The barn owner must make written request of payment and the non payment has to go on for several months.
Most likely, there would be some notice of the public auction.
This site has a list of all state laws, but I don't know how up to date it is -
http://asci.uvm.edu/equine/law/lien/lien.htm