NO school has ever dropped down from 1A to 1AA, you want ULL to be the first?
Several teams moved down in 1982 due to attendance restrictions being placed on teams (most notably the entire Ivy League moving down to IAA, Yale could have stayed but chose to move voluntarily along with rest of league). Several of these teams have since moved back up to FBS level.
Only two teams from the Southland Conference (which moved down to IAA in 1982) supposedly met the new guidelines in 1981, ULL and McNeese State. ULL moved to independent status for 1982 to avoid the move down, McNeese (similar to Yale) chose to move down along with the rest of the Southland to IAA starting in 1982 (a decision many fans question to this very day).