I'm not sure I understand you correctly, because (to me) "diplomacy section" and "foreign advisor" are the same thing.
I can think of two possibilities how seemingly dead rivals could appear to still be in the game. One is the option to show dead civilizations on the scoreboard (their score will then be displayed although the civs themselves are gone). The second is the option "Require complete kills", in this case rivals will stay in game even if they have no cities anymore, until you killed their last unit. Not sure whether one of these applies to your situation though.
By this i mean that i can go to the Diplomacy section within the Worldbuilder and they are there, yet i cannot find them on the map...
They appear in game turns for the usual 'Please aid with war'. Yet they are not on the Foreign Advisor display.