Indeed, a remnant still dwelt there of the Dunedain, the kings of Men that came over the Sea out of Westernesse; but they were dwindling fast and the lands of their North Kingdom were falling far and wide into waste.
My dear Frodo, that is just what the Rangers are: the last remnant in the North of the great people, the Men of the West.
Only a remnant of our eastern force came back, destroying the last bridge that still stood amid the ruins of Osgiliath.
The marauding orcs had been waylaid and almost all destroyed; the remnant had fled westward towards the mountains, and were being pursued.
Every now and again they made efforts to speak of other things, of their long road and many adventures; they questioned Aragorn concerning the realm of Gondor and its ancient history, and the remnants of its great works that could still be seen in this strange border-land of the Emyn Muil: the stone kings and the seats of Lhaw and Hen, and the great Stair beside the falls of Rauros.
There are no more uses of "remnant" in the book.
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They are working to eliminate remnants of al-Qaeda in that area.