OED Online says that " fag " is a shortened version of " fag-end ", which originally meant " [ t ] he last part of a piece of cloth; the part that hangs loose, often of coarser texture than the rest " or " [ o ] f a rope : An untwisted end ", and then by transference came to mean " [ t ] he last part or remnant of anything, after the best has been used " and " " spec ."
