A reinforced product, which can be used especially for reinforcing a finished rubber article, comprises one or more textile or metallic reinforcing thread(s), said thread(s) being covered with a sheath comprising a thermoplastic polymer composition, the sheathed thread(s) being themselves embedded in a rubber composition referred to as coating rubber, characterized in that this coating rubber is a composition based on at least one diene elastomer, a reinforcing filler, and a sulfur-based vulcanization system, which system comprises a vulcanization accelerator having a vulcanization initiation time, referred to as “t0”, of less than 3.5 minutes, preferably of less than or equal to 3 minutes.