A fruitless errand. It should be written sleaveless, as
it comes from sleave, ravelled thread, or the raw-edge of silk.
In Troilus and Cressida, Thersi'tës the railer calls Patroclus
an “idle immaterial skein of sleive silk” (v. 1).
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894