Yes, it does happen as I suggested in my original post, but you really want to avoid that last minute application/acceptance if at all possible.
A lot of the students accepted at the last minute don't really know what they are getting into and might struggle, or, even worse, realize they aren't truly interested in podiatry after they have started. Sure, there are some good ones who jump in under the wire and do fine, but they have also hurt themselves by applying late since most or all scholarships are spoken for by the time they're accepted.