Not found in Classical Latin. First recorded in the Capitularies of Charlemagne, probably from Frankish *drapi, *drāpi (“that which is fulled, drabcloth”) from Proto-Germanic *drap-, *drēp- (“something beaten”), from *drepaną (“to beat, strike”), from Proto-Indo-European *dhrebh- (“to beat, crush, make or become thick”). Cognate with English drub (“to beat”), Middle Low German drapen (“to strike, manage, work”), German treffen (“to meet”), Swedish dräpa (“to slay”). More at drub.
Compare Medieval Latin alternative form trapus (Spanish trapo), possibly from or influenced by Frankish *traba, *trapa (“cloth, thread, rag”), from Proto-Germanic *trabō, *trafą, *trēb (“fringe, rags”), from Proto-Indo-European *drāp-, *drāb- (“rag”). Cognate with Old High German traba (“fringe, tatters, thread”), Old Norse traf (“headscarf”), Middle English trappe (“trappings, personal belongings”), Middle English trappen (“to outfit, deck”).
Alternate sources cite possible derivation from an unrecorded word of Gaulish origin.