Any member of a sorority/fraternity can request to be removed from the rolls. It just depends upon who does the research where intake is involved. The fraternities to a better job of blackballing so this does not happen as often as in sororities.
I never knew anybody who did it, though, because in the part of the south where I went to school, they had a tendency to blackball people who had submitted applications to other sororities.
I think anyone who would leave one NPHC sorority to pledge another does the organization she leaves much more good than the organization she goes on to pledge.
TRSimon