...when a number of Chicago-based players transferred en masse and later laumched a lawsuit against an assistant coach for some form of "...ism." I believe it was settled out of court, but the assistant coach left a lot earlier than that. Here's an article on it. Ironically, at the time it was written, Ms. White fully expected to not play last season.
White and her dad were supportive of the head coach, but a few other players bolted, leaving her the stud on a very thin team. She did everything from rebound to shoot the most threes...all as a center.
While we'll never know what was in the exact petition, my guess is it cited that White was a good soldier. Apparently the NCCA goes back to the "host" (or the school the transfer is leaving) school for their input and I'm guessing Illinois cited White's hanging around for a year to keep the ship afloat.
In the case of Shepard, I think a lot will depend on what the current athletic director/2nd year coach feeds back to the NCAA. We'll see.