And came there never again as a living man.

[Gordis]

I think it is the same sort of seemingly ambiguous, poetic statement as the words about the Witch-King:

But lo! the mantle and hauberk were empty. Shapeless they lay now on the ground, torn and tumbled; and a cry went up into the shuddering air, and faded to a shrill wailing, passing with the wind, a voice bodiless and thin that died, and was swallowed up, and was never heard again in that age of this world.

The ultimate fate of Men remains a big unanswered question...