The captivity of Kib was not one of complete imprisonment, as he is able to father a son. Of course that son would also have been in captivity. The political strategy appears to have been one that did kept Kib as a token king, and perhaps even allowed Corihor to presume to rule under combined authority, borrowing authority from Kib who was his captive, and still alive. Of course the reference to Kib for authority would have had no substance, but the conceptual tie may have been important.