The following is inspired by the faint possibility of a 7-6 UCLA team playing in the Rose Bowl (oops, Oregon just scored another touchdown...).
Suppose a Big Ten team (Let's say Indiana just for fun) starts the season with four straight non-conference losses. Also suppose that Indiana goes 3-5 in conference play but still wins the Leaders division. This is not impossible - if every Leaders team loses every game against the Legends division, and each team goes either 3-2 or 2-3 in intra-Leaders games, then the division winner will be whichever 3-2 team wins the tiebreaker.
That would make Indiana 3-9 after the regular season but still playing in the championship game. Suppose they win. Their record goes to 4-9, and as the winner of the Big Ten championship game, they are awarded a spot in the Rose Bowl.
Or are they? They don't have six wins, so they're not even bowl eligible. So what happens?