Killing Nazgûl is not easy. If they are stabbed with a blade of Westernsee, their impotent spirits retreat back to Sauron. ("The Witch-king had been reduced to impotence." - Letter #246, Tolkien Letters, p. 331) In fact, they appear to be still living AFTER THE RING IS DESTROYED, a thing that is overlooked often times. For those of you who watched the film, you might have wondered why the Eight Nazgûl are still flying about after the Ring is destroyed, and only perished in the flames.
In this selection of text taken from Return of the King, Gollum has just gone over the brink with the One Ring, and Barad-dûr is falling. It appears that the Nazgûl still live, bodies and all, even though the Ring has been destroyed. They only perish in the fires of Mount Doom as they fly towards it. I can get no other interpretation of it, and this conclusion is supported by Tolkien's earlier outlines.
"And with that, even as his eyes were lifted up to gloat on his prize, [Gollum] stepped too far, toppled, wavered for a moment on the brink, and then with a shriek he fell. Out of the depths came his last wail Precious, and he was gone.
"There was a roar and a great confusion of noise. Fires leaped up and licked the roof. The throbbing grew to a great tumult, and the Mountain shook. Sam ran to Frodo and picked him up and carried him out to the door. And there upon the dark threshold of the Sammath Naur, high above the plains of Mordor, such wonder and terror came on him that he stood still forgetting all else, and gazed as one turned to stone.
"A brief vision he had of a swirling cloud, and in the midst of it towers and battlements, tall as hills, founded upon a mighty mountain-throne above immeasurable pits; great courts and dungeons, eyeless prisons sheer as cliffs, and gaping gates of steel and adamant: and then all passed. Towers fell and mountains slid; walls crumbled and melted, crashing down; vast spires of smoke and spouting steams went billowing up, up, until they toppled like an overwhelming wave, and its wild crest curled and came foaming down upon the land. And then at last over the miles between there came a rumble, rising to a deafening crash and roar; the earth shook, and the plain heaved and cracked, and Orodruin reeled. Fire belched from its riven summit. The skies burst into thunder seared with lightning. Down like lashing whips fell a torrent of black rain. And into the heart of the storm, with a cry that pierced all other sounds, tearing the clouds asunder, the Nazgûl came, shooting like flaming bolts, as caught in the fiery ruin of hill and sky they crackled, withered, and went out."
- Mount Doom, Return of the King, p. 224
Here are excerpts from some of Tolkien's earlier outlines that seems to verify this "life after the Ring" premise. This is Version I, written sometime around 1939-1941.
Perhaps better would be to make Gollum repent in a way. He is utterly wretched, and commits suicide. Gollum has it, he cried. No one else shall have it. I will destroy you all. He leaps into crack. Fire goes mad. Frodo is like to be destroyed.
Nazgûl shape at the door. Frodo is caught in the fire-chamber and cannot get out!
Here we all end together, said the Ring Wraith.
Frodo is too weary and lifeless to say nay.
You first, said a voice, and Sam (with Sting?) stabs the Black Rider from behind.
Frodo and Sam escape and flee down mountain-side. But they could not escape the running molten lava. They see Eagles driving the Nazgûl. Eagles rescue them.
- The Story of Sam and Frodo in Mordor, Version I, Sauron Defeated, p. 5
Here is Version II, which is more complicated than Version I, but shows the Witch-king as still around after the Ring goes into the fire.
"Frodo puts on Ring! A great cry rings out. A great shadow swoops down from Baraddur, like a bird. The Wizard King is coming. Frodo feels him - the one who stabbed him under Weathertop. He is wearing Ring and has been seen. He struggles to take Ring off and cannot. The Nazgûl draws near as swift as storm. Frodo's one idea is to escape it, and without thinking of his errand he now flies into the Chamber of Fire. A great fissure goes across it from left to right. Fire boils in it. All goes dark to Frodo and he falls on his knees. At that moment Gollum arrives panting and grabs at the Ring. That rouses Frodo, and they fight on the brink of the chasm. Gollum breaks Frodo's finger and gets Ring. Frodo falls in swoon. But Sam who has now arrived rushes in suddenly and pushes Gollum over the brink. Gollum and Ring go into the Fire together. The Mountain boils and erupts. Barad-dur falls. A great dust and a dark shadow floats away on NE from the rising SW wind. Frodo suddenly thinks he can hear and smell Sea. A dreadful shuddering cry is borne away and until it dies far off all men and things stand still.
"Frodo turns and sees door blocked by Wizard King. The mountain begins to erupt and crumble. Here we will perish together, said the Wizard King. But Frodo draws Sting. He no longer has any fear whatsoever. He is master of the Black Riders. He commands the Black Rider to follow the Ring his master and drives it into the fire."
-The Story of Sam and Frodo in Mordor, Version II, Sauron Defeated, p. 6-7
At least the movie got some things right. This quote, taken from a movie companion book which is strictly based upon the films, explains "life after the Ring" perhaps better than I can.
"When Aragorn led his army to the Black Gate the Nazgûl were part of the host that attacked them there, but they were commanded by Sauron to fly to Mount Doom when he perceived what was about to happen. Yet despite their great speed they were too late, and perished in the inferno caused by their master's destruction."
- The Lord of the Rings Weapons and Warfare by Chris Smith, p. 167
A VERY interesting question!
I agree that the Nazgûl were NOT destroyed in the same instant that the ONE Ring melted. The quotes Angmar gave are quite convincing.
But why?
I think that this was because the Nine Nazgûl were NOT DIRECTLY DEPENDENT on the ONE. Sauron was. He made his shape again, wielding the One, after his body perished in the fall of Númenor. It took about 100 years. He had great difficulties reshaping himself in the Third Age because he could not WIELD the One. He was able to re-flesh himself in about 1500-2000 years, because the One still existed somewhere. I think he used the remaining Dwarven rings for that, which he gradually collected while he sat in Dol Guldur.
Now the Nazgûl were dependent on the NINE rings (not the One) in much the same way. I think, IF Sauron would just go to Orodruin and throw one of the Nine Rings into the Fire, the corresponding Nazgûl would be killed on the spot, his body falling to nothing, his clothes left behind, and his spirit going to Mandos.
I think the Nazgûl existed as long as their NAZGÛL RINGS existed and HAD POWER. The last part is very important. The Nine, the Seven and the Three all depended on the One. When the One was destroyed, what happened to the other Rings? Sauron had the remaining Seven and all the Nine in his physical possession at the moment of the Fall of Barad Dûr. The One was melted, but the Seven and Nine were not! Most likely they were simply BURIED under the ruins of Barad-Dûr.
We know what happened with the Three. They lost their power GRADUALLY after the destruction of the One. Lórien, made with the power of Nenya, had not disappeared in a blast; the same is also true with Rivendell. Both gradually WANED. Bilbo, though he was now very old for a hobbit, didn't die immediately, but started to show his age considerably, and was waning fast.
So if we consider that, with the destruction of the Ruling Ring, the power of the Nine gradually waned, then the Nazgûl were doomed all the same. Sooner or later, the Nine Rings would loose their power and that's how the would Nazgûl end.
That's why, perhaps, the Witch-King sounded so suicidal: "Here we will perish together," instead of just throwing the little hobbit into the chasm and saving his own "eternal" life.