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Wiktionary
fag end

n. (alt form of fag-end English)

WordNet
fag end
  1. n. the time of the last part of something; "the fag end of this crisis-ridden century"; "the tail of the storm" [syn: tail, tail end]

  2. the frayed end of a length of cloth or rope

Usage examples of "fag end".

It seemed he was in a cell with a couple of lads only a little older than him, there had been some disagreement and a burning fag end had been stubbed out under Joby's eye.

All that was missing was his clip of pens and a fag end dangling from his lip.