"wear off by rubbing," c. 1400, from Old French fraiier, froiier "to rub against, scrape; thrust against" (also in reference to copulation), from Latin fricare "to rub, rub down" (see friction). Intransitive sense "to ravel out" (of fabric, etc.) is from 1721. The noun meaning "a frayed place in a garment" is from 1620s. Related: Frayed; fraying.
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<a href="https://www.etymonline.com/word/Frayed">Etymology of Frayed by etymonline</a>
Harper, D. (n.d.). Etymology of Frayed. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/Frayed