Did you really think you can kill the villain? Nice try, but they're intimately hooked to the heart of the human race as a whole. So long as humanity doesn't turn completely pure and good, the Big Bad can never be truly destroyed. Oh, sure, you might have put them down for this episode/game/movie/series, but the next time the world's malice builds up again, they'll be right Back from the Dead with a new Evil Plan.
In essence, this is Evil's answer to As Long as There Is One Man and Hope Springs Eternal; the Big Bad is The Heartless for all of mankind. They typically weave the revelation into their Final Speech, just before the hero puts them down.
While this usually doesn't mean much from a story standpoint (they're still dead), it can make for a Bittersweet Ending — the heroes went through all that for what? If the heroes are really unlucky, the Balance Between Good and Evil will demand that they replace the Big Bad that they just slew.
For the really determined hero who has accepted the fate of fighting this evil, the classic response is, "And so will I." as a challenge to the villain any time, anywhere. Otherwise the only decent reply is The War Has Just Begun. Sometimes, "sealing" the villain provides a more long-term solution than killing them. Yeah, they can (and probably will) escape eventually, but it'll take longer than it would to resurrect them.
This trope normally comes after Abstract Apotheosis, in which the character (upon death or other means) uses their self as a form of representation. For example, in the case of the Big Bad becoming this form of hatred, this can be appropriately accompanied with a Madness Mantra and/or Badass Boast.
Compare Staying Alive, where the villain doesn't even die. Compare Emotion Eater, which As Long as There Is Evil can be considered a variation of. Contrast As Long as There Is One Man; the heroic response but without the resurrection. Compare Good Needs Evil, Inherent in the System and In Your Nature to Destroy Yourselves. Likely a God of Evil, Made of Evil, or an Unseen Evil. See We Will Meet Again for the more prosaic variant. See Evil Only Has to Win Once for the extreme danger a single villain victory poses.
