Sadly, it happens. The economy changes, living circumstances change, family dynamics change, people lose jobs, move away, etc. Availability and cost of hay and concentrates for horses change... People who once were able to afford their horses and spend time with them find themselves in a position where they are struggling financially, or otherwise, and maybe owning a horse is no longer the best option for that person, or their horse.
When is "enough" enough? This is clearly a slippery-slope, as people view horses as family members quite often. If that is the case, then it may be best to view the horse as a family member that has special needs - and ask yourself if you are the best person to provide those needs? If it were your grandmother, and she needed "x,y and z" in terms of care, and you could only provide "z", but you know your sibling or a facility could provide "x, y and z", you wouldn't just dump your grandma in a back room and hope for the best. You'd likely contact the sibling or facility (I'd hope) and say "look, grandma needs help, and I'm unable to provide it. Lets take care of this!" Unfortunately, some people choose to do that with their equine family members - the equivalent of locking them in a room and hoping that by "not seeing" it isn't happening. It doesn't have to be that way... and it shouldn't be that way.
If you can't afford to pay board (or keep your horses and feed them sufficiently at home), then the answer is clearly "no", you should not keep holding on. Are you willing to sacrifice the standard of care of the horses in order to "afford" to keep them? If so, how poor of care are you willing to go with?
Leaving horses at a facility and failing to pay for their care and keep does not make you a horse owner. Neither does paying a minimal amount for such poor care that animal control steps in. There comes a time for some people
when horse ownership needs to end - that doesn't mean it can't happen again in the future.
It is an owner's responsibility to have a plan in place, and to recognize when the need arises for new homes to be found for their horses.
What are some good questions for horse owners to ask themselves regarding this heartwrenching, but sometimes inevitable, decision?