Remnants of an older time they be, living few and secretly, wild and wary as the beasts.
Mean folk shall rule the last remnant of the Kings of Men, lurking in the hills until all are hounded out.
They were the remnant of the guard that was kept at that point where the way from Anorien and Rohan ran into the townlands: Ingold led them, the same who had admitted Gandalf and Pippin less than five days before, while the sun still rose and there was hope in the morning.
For some had laboured and fought much with the remnants of the Easterlings and Southrons, until all were subdued.
Then he drew his forces off, encircling the last remnant of the Men in a wide ring of archers.
The task of hunting out the last remnant of the ruffians was left to Merry and Pippin, and it was soon done.
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.
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.