The answer is written clearly in the Official FAQ:
Q: If the Citadel’s power is lost or discarded, are the citadels discarded or not?
A: No, they remain in play, but serve no function.
The FAQ is woefully incomplete here (as usual) and thus doesn't really answer the question.
The OP is talking about the Wild Sorcerer flare, which says "you may force the main players to trade alien powers with each other. They keep their new powers after the encounter ends." This flare is essentially a mini version of the Changeling power. Changeling includes a crucial piece of information that Wild Sorcerer is missing, and we need to understand that Wild Sorcerer (and indeed, any power-swapping effect) has the following implied consequence:
"When swapping alien powers, you get all facets of that power – e.g., the Miser's hoard, the Warrior's tokens, The Claw's claw, etc."
So when the FAQ says the citadel cards "serve no function", this should be understood to mean only in the context where the CItadel power has been "lost" from play — nobody is being that alien any more. But when when somebody else swaps for the power, he gets the citadels too.
It has to work like this or things will break. For example, if Wild Sorcerer were to swap The Claw, its new owner would have no claw card (and no way to get one), and thus the power would be useless for the rest of the game.