This is the hard part. There will have to be the right kind of pressure, but this has to be done if she won’t pay and move the horse.
Understandable that owners may see their horses emotionally as pets. And be very attached.
BUT – she can’t afford to care for this very expensive animal. One option to approach to the owner may be just that.
What if the horse needs surgery – how will she pay? An extended treatment for something like EPM? Or some injury? (It’s a horse, it can find a way to injure itself or be sick even if it’s relaxing and doing nothing.)
(If she says she can pay for that … then she can pay the back board.)
She is already not doing basic vet and farrier. Point out that the farrier neglect especially causes suffering for the horse, even at a low level, as his feet are out of balance and stressing muscles and tendons. Gently point out to her that this is “neglect”. Use that word more than once. It will upset her, but she needs to hear it.
And so on. Focus less on what she owes, but on the impact on the horse.
Immediate, current impacts on the horse are very important to emphasize. The owner may be a bit short-sighted, focused only on today. Long-term health and injury possibilities need to be raised as a concern, also.
And finally, that relinquishing the horse solves all of these problems. The horse will get care, the neglect will be caught up. This horse she loves will go on to live his best life.
She will be doing the best, kindest, most loving thing for the horse by relinquishing him.
Definitely better than an auction if the BO’s have to take him legally.
Make these things her choices – relinquish to best life, or hold out until he goes to auction.
One reason she isn’t coming to see the horse may be that she is having problems facing the sight of her horse’s feet, etc. Doesn’t want to see the evidence of her part in neglect. As well as avoiding uncomfortable encounters with the homeowners.
But whatever the approach … sounds like she needs to pay and move the horse if she won’t relinquish it. The BO’s can decide which is their preferred outcome.