West Point also has a scholarship program through the Association of Graduates.
There are some differences between academies but generally they all work the same way -
Candidates who are not offered appointments for whatever reason - (could be academics, low SAT's, little athletics) are selected by admissions to receive a scholarship from the Foundation or AOG to attend a prep program for one year.
The Foundation or AOG either selects the school or gives you a list of schools from which to choose. The candidate re-applies and if they are successful in the prep program then they are offered an appointment.
It is an excellent opportunity for many candidates. The admissions office basically holds your spot for the next class and it is yours "to lose".