At this point
Sting is with
Sam, as can be seen in this paragraph from the chapter
Mount Doom where they're tossing stuff away so they don't have to pack it any more.
"He came back to
Frodo, and then of his elven-rope he cut a short piece to serve his master as a girdle and bind
the grey cloak close about his waist. The rest he carefully coiled and put back in his pack. Beside that he kept only the remnants of their
waybread and the water-bottle,
and Sting still hanging by his belt; and hidden away in a pocket of his tunic next his breast the
phial of Galadriel and the little box that she gave him for his own."
So Sam is packing Frodo's stuff as well as his own now.
The question might be asked why Sam did not rush forward and help Frodo when he was tussling with
Gollum at the brink of the chasm's edge.
But we get the sense that Sam, having been knocked down, getting up 'dazed and with blood streaming down his head', saw all that was transpiring in a very short span of time, and did not have presence of mind nor time to either react, or act, given what he was seeing.
Thus ends Gollum... not by the thrust of Sting into the murk and mire of his innards, but by his own glee and lust at fulfilling at last his desire to repossess
the Ring,
and get betrayed by it. (Or by an even wiser and greater power, as it were, the ring not 'willing' itself to be destroyed.)
To Ent, a much more satisfactory ending than simply being gutted into the bargain.
