It has NOT happened from 2002 to the present. That's as far as the kenpom database goes. Since 2002, only three power V teams have gone winless in basketball conference games:
- Texas A&M in he Big 12 in 2004
- Oregon State in the Pac 10 in 2008
- TCU in the Big 12 in 2014
All of those schools had bowl seasons in football those years.
Over the same time period (2002 to present), the most pathetic combined football/basketball record that I could find was Indiana in 2009. In the wake of the Kelvin Sampson scandal, they went 1-17 in basketball and 1-7 in football. (2-24). BC has a great shot to beat that mark of futility. FWIW, WF is currently 2-16 in those two sports; so, the Deacs still have some work to go to avoid tying Indiana.