I would think a pawn should automatically be ejected from the fellowship (not a right as a non paying member to be in any fellowships) and then the next in line rook should take over.
The rank should be set automatically by join date of the fellowship (ie longest serving rook is the next in line) however, this rank structure should be able to be changed by the Big Boss so that he.she can control who gets the reins when they get omitted