Regulates the turnover of the sigma S factor (RpoS) by promoting its proteolysis in exponentially growing cells. Acts by binding and delivering RpoS to the ClpXP protease. RssB is not co-degraded with RpoS, but is released from the complex and can initiate a new cycle of RpoS recognition and degradation. Binds to RpoS. Phosphorylated. Phosphorylation stimulates the interaction with RpoS and, therefore, the proteolysis of RpoS. Belongs to the RssB family.