4.5. The Destruction of the Ring
At the brink of the Cracks of Doom, Frodo claims the Ring for his own and puts it on. The Dark Lord, in a dreadful realisation that the Ring is not where he thought it was, being wielded by one of the Captains of the West at Black Gate, bends all of his power to Mount Doom. Sam, having been struck from behind by Gollum;
"saw a strange and terrible thing. Gollum on the edge of the abyss was fighting like a mad thing with an unseen foe...... Sam saw Gollum's long hands draw upwards to his mouth; his white fangs gleamed, and then snapped
as they bit. Frodo gave a cry, and there he was, fallen upon his knees at the chasm's edge. But Gollum, dancing like a mad thing, held aloft the ring, a finger still thrust within its circle. It shone now as if verily it
was wrought of living fire.
It has been suggested that this ending is too facile, and that too much is left to chance. Yet in my view it is totally consistent with Tolkien's "world-view" with the nature of the Ring and the nature of evil.
I have already observed that there are a number of powers at work in Middle-earth, and that the powers of Good operate to set the environment within which free people may make the choices that can determine their own fate and that of others. Gandalf hints;
"Many that live deserve death. And some that die deserve life. Can you give it to them? Then do not be too eager to deal out death in judgement. For even the wise cannot see all ends. I have not much hope that Gollum can be cured before he dies, but there is a chance of it. And he is bound up with the fate of the Ring. My heart tells me that he has some part to play yet, for good or ill, before the end; and when that comes, the pity of Bilbo may rule the fate of many." 
Indeed, the ultimate eucatastrophe, and the final triumph of good over evil is presaged in The Silmarillion, when the glory of the Music of Iluvatar will be revealed to all. Thus, there is a certain degree of fate within the Tolkien cosmos, and the circumstances within which the events leading up to the destruction of the Ring take place are not all ordained purely by chance. Certainly there are many occasions when choice may influence events, and it is Frodo's choice to claim the Ring that sets the stage for Gollum's actions. Yet even if Frodo had not claimed the Ring, it is consistent with what has gone before, that Gollum would attempt to seize the Ring at the last post. And because he was so broken and corrupted by the Ring and his lust for it, his ecstatic triumph would have had the desired result - the end of the Ring.
This leads us to the most significant issue that surrounds the destruction of the Ring, and that is that Evil embodied in the Evil object, because it is a destructive force, carries within it the seeds and potential for its own destruction.
"But the only measure that he knows is desire, desire for power; and so he judges all hearts. Into his heart the thought will not enter that any will refuse it, that having the Ring we may seek to destroy it. If we seek this we shall put him out of reckoning." 
"But the evil they work according to their maker's design turns often to good that he did not intend, and even to his loss and defeat." 
These two comments give clues as to the self-destructive nature of evil. Consider the history of the Ring. It slips off Isildur's finger and betrays him. We know that the Ring works to try and get back to its Master. Deagol finds the Ring, and it is taken from him by Gollum. The evil of the Ring corrupts Gollum utterly. The power of Sauron as Necromancer arises in Mirkwood and the Ring once again stirs. Bilbo finds the Ring, and Gollum, having been deprived of the Precious, seeks to regain it.
Sauron is aware that the Ring is abroad, and that it is in the hands firstly of hobbits and latterly of Men and Elves. He becomes aware of Aragorn as Heir of Isildur when Aragorn reveals himself to Sauron in the Palantir of Orthanc. Clearly, Sauron believes that the Ring will be wielded by Aragorn, and although he has no positive proof, the defeat of his forces at the Pelennor Fields and the end of the Black Captain could lead him to infer that the Ring is in the hands of those who are using main force.
Indeed, the thought of anyone wanting to destroy the Ring has never occurred to Sauron. So obsessed is he with retrieving his power that he cannot conceive that anyone would want to destroy it, but, like him, would desire to have it and use it. This is the very reason why the destruction of the Ring is mooted at Rivendell. And Sauron's self-deception, and the consequences of it become clear when Frodo claims the Ring.
"(A)nd the magnitude of his own folly was revealed to him in a blinding flash, and all the devices of his enemies were at last laid bare. Then his wrath blazed in a consuming flame, but his fear rose like a vast black
smoke to choke him. For he knew the deadly peril and the thread upon which his doom now hung.
The last act played out at the Cracks of Doom demonstrates how the Ring works to its own end. It is at the heart of Sauron's realm, seeking its master. It is claimed by one who does not have the strength to wield it. It wishes to return to its master. Into the equation steps the individual whom it has corrupted, and whose desire for the Ring is all-consuming. Gollum takes the Ring, and the way is open for the Nazgul, flying in a storm of wings, to recover the Ring for Sauron. But so ecstatic is Gollum that he has recovered this object that has so corrupted him, that in gloating triumph he missteps. It is the Ring that has been responsible for its own downfall. In setting the scene for departing from Frodo, it has failed to see how the individual that it has ruined will act. Evil could not foresee that its own nature would turn against it to its ruin. Thus, it leads to its own loss and defeat.
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The Tolkien Encyclopedia
The Art of Tolkien
One Ring to Rule Them All by David Harvey
Hypertextual System by FMI Publishing, 1995