Melkor indeed does return to the circles of the world. He is 'at large' for the
Dagor Dagorath, the final battle of Tolkien's mythology. To steal a quote used by our fellow forum poster Legalos,
Quote:
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Manwë will not descend from the Mountain until Dagor Dagorath, and the coming of the End, when Melkor returns.
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...and this is all contained within the Silmarillion, which is a very good place to start in search of answers for such questions.
With all this talk of Doomsday, arm-a-geddin' out of here...