It reminds me of busy. Same thing.
A buyback pony is one that is preselected by the committee to stay in the herd, usually for breeding purposes. This ensures that the line stays strong and they breed in the best parts of it. Much like any breeder, dog or such.
They are put up for auction, with everyone knowing ahead of time it is a buyback and it is bid on and usually, a group or a philanthropist will throw money at it to help support the cause. My family went in with a few and sponsored a pony a couple of years ago. It allows you to register the name and you have privileges to go to parts of the island reserved for trustees. Small potatoes, but, we do love our ponies. :)
That's a very cool way to raise funds and you get extra access to certain areas. Nice of you and the family to support this idea.
I wonder if we have the same thing over here? I'll ask my horse owning friend Lucy.