Green’s Dictionary of Slang

fag-end adj.

final, last.

1885		Bulletin (Sydney) 16 May 9/1: The whole affair wound up with a farce, ‘You’ll find him out.’ As a rule, when the fag-end farce comes in at ‘nigger’ entertainment, you see most of the middle-aged, respectably dressed people make for the door.
2000		Observer Rev. 9 Jan. 13: It revels in the absurdities of the century’s fag-end decade.