I heard of this kind of situation occuring with a PNM I knew personally. She went through recruitment and ended up getting cut after the first round by every chapter but "chapter A", a smaller, newer group that was considered lower tier. She was a fun, sweet, pretty girl but had made the mistake of ticking off some greeks by not keeping her nose clean during her first semester (they have deferred rush).
To her credit she was consistently polite to chapter A's rushers, but obviously felt that she was "above" them. She dropped out after pref but was snap bid the next day by the higher-tier chapter B, who had cut too heavily early on and missed quota by a few (which is rare for them). She accepted and the you-know-what hit the fan. Usually no one knows or cares if someone was a snap bid, but earlier in recruitment there were girls in that chapter that did not want her there and fought hard to have her cut, so when she showed up on bid day everyone was shocked. The advisor knew this, but had snap bid her anyway without consulting the chapter so they wouldn't miss quota. The really sad thing is that this PNM knew all of this (she shouldn't have, but she did) and STILL decided to join and stick it out. She had a pretty rough new member period because of all the drama and still has few friends in the chapter outside of her big & little. But she gets to wear the letters!
It was just so disappointing to me that a PNM would drop of out recruitment to avoid getting a bid from a lower-tier group that obviously wanted her, and then take a snap bid from a higher-tier group that just needed a warm body and had a sizeable contingent of girls who made it clear to her that she was not welcome.