Can a student-athlete on a sports scholarship be "reassigned" to some other type of a scholarship? If so, what other types?
I wouldn't use the term "reassigned", but yes.
See the bylaws, rule 15. Athletic Scholarships are year to year, and do not need to be renewed. Think of a walkon that gets one for his junior year because the team didn't use them all, he would likely not expect to retain it for his senior year.
If he qualified for certain other types of scholarships, he could still utilize them. Again, see bylaw 15.
However, anytime this happens, you can bet the NCAA goes over it with a fine tooth comb and making sure they are not athletic scholarships in disguise.
Also, few athletes in basketball/football would want to do this. Those athletic scholarships are full rides that include room and board, something that very few other scholarships come close to matching.