the last part or very end of something: the fag end of a rope.
the unfinished end of a piece of cloth; remnant.
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023
British Dictionary definitions for fag end
the last and worst part, esp when it is of little use
British informal the stub of a cigarette
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012