The Avatar Wika page on Professor Zei claims that he is still alive, trapped in the Library (Spirit World) for all eternity. That could be from his departing line, or it could be (as cited) from the Book 2 “Extras” where they would re-air the episode with Pop-Up-Video like facts.

On “City of Walls And Secrets” the 41st and 42nd pop ups are:

• Professor Zei was last seen in the episode “The Library”.
• And Professor Zei is most likely still in the library.

So there you go!

-Da7e-

EDIT: I assume you all know what Pop Up Video is, because if you don’t I am old and I’m trying to avoid that feeling.