Many explanations have been proposed for the function(s) of the POFs.
In Equus at least, one possible cause (not "function") is the "caveing-in" of the malar region when it is no more "sustained" by cheek teeth because they are too worn.

As example, here is the skull of an E. caballus found inside a Kurgan (MGRI 1772, Tiraspol, Moldau) and its upper cheek teeth.