Morgoth was thrust through the "Doors of Night" into the Void beyond Ea, where he dwells now "shapeless and powerless."
But has been well written in one place: "Yet his terrible example was to have lasting consequences, for not even the mightiest blow could destroy the
evil now awake in
Middle-earth." Tyler, J. E. A.. The Complete
Tolkien Companion (p. 530). St. Martin's Publishing Group. Kindle Edition.
Sauron too was 'cast into the Void forever', and somewhere it is written he "shared in the same fate as his master." (Still looking for that.)
We also read: "Then Sauron failed, and he was utterly vanquished and passed away like a shadow of malice;" Tolkien, J.R.R..
The Silmarillion (p. 307). HarperCollins. Kindle Edition.
Yet here too: "For though Sauron had passed, the hatreds and evils that he bred had not died, and the King of the West had many enemies to subdue before
the White Tree could grow in peace." Tolkien, J.R.R..
The Lord Of The Rings (p. 1071). HarperCollins. Kindle Edition.
It is prophesied that
Melkor will return at some point yet again. Though Sauron is not mentioned in the prophecy that I know of, it could well be that Melkor will not come alone... but this is speculation.
As the "effects" of the evil of Melkor remained and Sauron became the supreme evil One, so now the "effects" of Sauron remain, and there are always those who try to become the new supreme evil One. It will always be so until the end.