They don't. Lawvol was correct and I was wrong. I thought Poole leaving Kentucky freed up a scholly. Not so as the scholarship awarded reflects against your headcount for the entire academic year even though you may transfer out during the year. Here is the NCAA bylaw describing this:
184.108.40.206 Cancellation of Aid. Once an individual becomes a counter in a head-count sport (see Bylaws
15.5.2, 15.5.4, 15.5.5, 15.5.7), the individual normally continues as a counter for the remainder of the academic
year. However, if he or she voluntarily withdraws from the team prior to the first day of classes or before the first
contest of the season (whichever is earlier) and releases the institution from its obligation to provide financial aid,
the individual no longer would be considered a counter (see Bylaws 220.127.116.11 and 18.104.22.168.1).
Also according to this bylaw it would seem academic scholarships may not allow him to play (not sure though):
22.214.171.124.1.2 Institutional Academic Scholarships. Institutional academic scholarships that are part of an institutions normal arrangements for academic scholarships, based solely on the recipients academic record at the certifying institution, awarded independently of athletics interests and in amounts consistent with the pattern of all such awards made by the institution, are exempt from an institutions equivalency computation, provided the recipient has completed at least one academic year of full-time enrollment at the
certifying institution and has achieved a cumulative grade-point average of at least 3.300 (on a 4.000 scale) at the certifying institution.
It would appear to me that UK and Memphis are only an option if he walks on and pays his own way. I may be wrong though.