State laws vary but in many states, yes, the horse can be held and sold.
"4. Most states require you to retain physical possession of the horse to “perfect” your lien. If the horse is gone, so is your lien. This requires you to put the owner on notice of the lien and to ALSO prohibit (in writing) the owner from removing the horse while the lien is declared. This can be problematic, where owners often try to “spirit” the horse away without payment OR permission. Seek legal counsel on how you can prevent this. Include a contract clause stating the unauthorized removal of a horse that has been liened constitutes a trespass to property. Notify the client in writing again, at the time the lien is declared, that removal without satisfaction of the debt is prohibited and will be treated as a trespass. Also consider relocating the horse in various stalls or in a more secure area of the stable until payment is resolved.
Non-possessory states permit the lien to follow the horse—regardless of location—until satisfied." https://stablemanagement.com/articles/stable-owners-learn-your-lien-laws
“At the heart of the stablemen’s laws is a lien. A “lien” is a legal claim to hold onto or to sell certain types of property belonging to someone else, as security for payment of a debt. When applied to a horse, the lien makes the horse become collateral to secure the payment of board (and sometimes, depending on the law, to secure payment of related charges, such as training fees). Those who hold liens often have the power to hold onto the property and to keep it from being sold, transferred, or moved. What also makes liens especially powerful is that they can potentially allow the one who holds them the right to sell off the property.” https://www.equinelawblog.com/Stablemens-Lien-Laws-What-They-Are
ETA VA lien law: § 18.2-188.1. Defrauding person having a lien on an animal; penalty.
It shall be unlawful to remove or cause any horse or other animal to be removed from the possession of the owner or keeper of a livery stable or other person having a lien on the horse or animal for keep, support and care pursuant to § 43-32, with intent to defraud or cheat the lienholder. A violation of this section shall be punishable as a Class 2 misdemeanor.