ND has put quite a few guys on medical scholarships, but it's usually the player's choice to take the medical and finish the ND degree, rather than transferring and trying to play somewhere else.
Ohio State (and every school, probably) has done the same, but they ALSO have a history of "forcing" medical scholarships on players that they want to process out when things get tight.
Jamel Dean early enrolled at Ohio State, but their numbers were getting tight near NSD... Dean enrolled, got his physical on campus, but then his history of knee problems in high school suddenly became an issue.
He was declared medically unfit by Ohio State's doctors, not even given a chance to have surgery and rehab for the year... duh, because that would've been a waste of a spot in a recruiting class that had four (!) other CB's. They told him he could stay at Ohio State on medical scholarship, or hit the road.
He got a second opinion, got his knee fixed up, and then went to Auburn and had a decent career. He's probably gonna be drafted this April.