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Sauron: Tol Sirion
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When Morgoth left Angband to corrupt the newly-created Men, Sauron directed the war against the Elves. He conquered the Elvish island of Tol Sirion, so that it became known as Tol-in-Gaurhoth, the Isle of Werewolves.
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While this version of the Moria Balrog's history was clearly rejected when Tolkien decided the Balrog should be the force which drove the Dwarves from Moria, it certainly demonstrates that Tolkien considered it possible for Balrogs to follow Sauron's orders. At that, there is at least one text mentioning such a situation;
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Beren himself fled southwards through the treacherous paths of the Ered Gorgoroth, and Sauron's army of werewolves failed to capture him. Fate drove Beren into Sauron's hands eventually, though: some years later as he travelled northward on the Quest of the Silmaril, Sauron captured him with Finrod and their companions and imprisoned them in Tol-in-Gaurhoth.
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Tolkien noted that Sauron was said "to have fallen below the point of ever recovering, though he had previously recovered. What is probably meant is that a 'wicked' spirit becomes fixed in a certain desire or ambition, and if it cannot repent then this desire becomes virtually its whole being. But the desire may be wholly beyond the weakness it has fallen to, and it will then be unable to withdraw its attention from the unobtainable desire, even to attend to itself. It will then remain for ever in impotent desire or memory of desire."[43] Thus Sauron was "damned" in the sense that he was "reduced to impotence, infinitely recessive."[44]
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Tol Sirion