An elongated protective textile sleeve for protecting elongate members and methods of constructing a fabric substrate therefore. The fabric substrate has a plurality of filamentary members either woven, knitted or braided with one another. At least some of the filamentary members of the substrate extend to cut edges and are fabricated of a multi-component material that includes a core of a first polymeric material and an outer sheath of a second polymeric material. The outer sheath is heat-fusible and the inner core is heat-settable. The outer sheaths of the filamentary members are heat fused at least in the regions near the cut edges to keep the cut edges from fraying or the filamentary members from pulling out of the substrate. The core is heat set to form the desired shape of the protective sleeve.