Associate Professor to Assistant Professor
Within one university this would be a demotion so it is possible but rare, and could happen if the appointment and ensuing titles were given by courtesy, i.e. the appointment is not a regular full-time appointment.  Rank associated with this courtesy appointment might then be tied to some specific commitments. 

I’ve never seen this happen for a regular position: I would guess that such demotion of a regular faculty member would lead to dismissal or resignation.  For courtesy appointments my experience is that these are either renewed or not, but I know of one place where such a “demotion” is technically possible.