Definitions for fag end
Random House Webster's College Dictionary
(n.)the last part or very end of something:
the fag end of a rope.
the unfinished end of a piece of cloth.
a remnant or scrap, esp. of cloth at the end of a bolt.
Origin of fag end:
1605–15; >ME fagge flap
fag end, tail, tail end(noun)
the time of the last part of something
"the fag end of this crisis-ridden century"; "the tail of the storm"
the frayed end of a length of cloth or rope