When do they stop? Probably shortly before their last interview date in January. I got offered an interview last year in the middle of January at a program I had completely forgotten I even applied to.
Think how people cancel interviews up until the last minute (it's a ton). Even at Michigan where they may temporarily have all their spots filled, I guarantee people will rearrange schedules and cancel and they will have to send out some more invites to fill them up. Happens all the time.