I've always been very careful about where my retirees go..sometimes it isn't possible of course, and yes, a bullet the best option. Even that isn't as easy as it used to be, and euthanasia by a vet is costly.
Now we have a number of re-homers , registered with NZTR ; it is, I guess, an attempt to 'do the right thing' but plenty of holes in the system for all that.
They get an admin fee for doing the paperwork, and a grant is available for outside practitioner fees, ie vet. But nothing to cover feed etc, and in the case of horses in poor shape, a costly exercise for the business. I can understand completely why they may refuse welfare cases, and also - although not ideal for either horse or new owner - why they are moved on in a matter of days sometimes. Nice pics of the animal jumping a fence and off they go as 'educated jumpers' .....not.
And once the horse is moved on to its new home, it then drops out of the system and there is no way to keep tracking it, unless the goodwill of the new purchaser runs to contacting the former trainer/owner.