This is going to vary wildly based on the program, of course.
Full-training programs will have a different approach than those that just require one lesson a week.
IME, a full training program will use the “training/lesson fees” portion of your monthly board towards any rehab labor they agree to take on, such as wrapping, hand walking, etc. But, they may not all agree to take on such rehab labor. The ones that do agree to provide rehab services, usually limit how long they’ll do so. I’ve seen mostly three to six months, some will go to a year. If the injury will require a longer time than that, they’ll recommend you go to an actual rehab facility. Some may be willing to hold your stall for a dry-stall fee. Most won’t hold the stall, period. If the injury is career ending, they’ll recommend you move to a retirement farm.
Programs that only require something like one lesson a month, it seems the COTH consensus (from other threads) is that they don’t let you use any monies paid towards training or lessons in another month, and they won’t discount you if you’re unable to take lessons. They may rehab the horse for you, at an additional cost. So, you can be okay with paying for unused lessons should an injury or something occur, or you can find somewhere else to go.
The ones that do not want to (or don’t have the capacity to) take on the rehab, will ask you to move the horse to a rehab facility. Same as above - some may be willing to hold your stall, more won’t.
I understand that this is a simpler business model. Personally, I don’t really like the idea of paying for services not received. I don’t board at training facilities that require any amount of training, I’m definitely none of these types of barn’s target demographic.