Euthanasia is a humane end to an animal's life. I think it is a responsible choice of the owner to have her put to sleep rather than shipping her to slaughter.
If she was to become a broodmare, where would her foals end up? Do we really need more horses, especially of a popular breed like TBs, one of which you can pick up for free any day?
Let the owner have her euthanized. It seems to be the best option. You can put your money towards taking a horse out of a neglectful, abusive or slaughter situation.