Dictionary.net

• fag'-end, n. the end of a web of cloth that hangs loose: the untwisted end of a rope: the refuse or meaner part of a thing.

1908 - Chambers's Twentieth Century Dictionary of the English Language
By Thomas Davidson

• n. An end of poorer quality or in a spoiled condition, as of a web of cloth, &c.;—the refuse or meaner part of any thing.

1871 - The Cabinet Dictionary of the English Language