The Collaborative International Dictionary
Fag-end \Fag"-end"\, n.
An end of poorer quality, or in a spoiled condition, as the coarser end of a web of cloth, the untwisted end of a rope, etc.
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The refuse or meaner part of anything.
The fag-end of business.
--Collier.
Wiktionary
alt. 1 last remnant 2 frayed end of a length of cloth or rope 3 The unsmoked end of a cigarette or cigar n. 1 last remnant 2 frayed end of a length of cloth or rope 3 The unsmoked end of a cigarette or cigar
Usage examples of "fag-end".
Time had come apart and tossed the hulking great ship like a fag-end into a vortex of alternities that threatened to tear it dimension from dimension.
Only once or twice has he taunted me with what sounds like the interesting sport of going into the gents in the Cauldhame Arms (or anywhere else, I suppose) and attacking the drowned fag-ends in the urinals with a stream of piss.
You can score points for the number of ceramic divisions you can move the butt over (with extra for actually getting it down the hole and extra for doing it from the far end of the gutter from the hole), for the amount of destruction caused - apparently it's very hard to get the little black cone at the bummed end to disintegrate - and, over the course of the evening, the number of fag-ends so dispatched.
They spoke of a General Abercrombie, who was to command them and a very considerable force gathered from all parts of India: it is difficult to make much sense of what they said, for their colonel was killed in the action, and the junior officers had only fag-ends of gossip.
Most of the rest of it was pink and purple skin, studded with the fag-ends of feathers, so that the net effect was of an oven-ready hairbrush.