From what I got from the subs, Satsuki's manifest said something like "erase the scholarship students"; this line has two interpretations; Satsuki intend to erase the scholarship system or erase the scholarship student as figure, i.e. as a target. Erasing the scholarship student figure means exactly what Triple_R has already explained in his last post. They will not work anymore and the money Satsuki saved from the abolished clubs will cover the difference with the tuition. The scholarships students won't exist anymore because they would be enrolled as normal students, sort of. I don't know how practical her idea is in detail, but if she had enough money it could work.
Now I'm curious to see what Pakojima will think up to have it both ways
They will open a bakery inside the school.