Fire retardents work by leaving salts in the treated material. Basically they are a salts combination in a carrier fluid. When it is sprayed onto a fabric it is absorbed and eventually the carrier fluid evaporates leaving the salts behind. It is these salts which inhibit burning by causing any flames to splutter and die out.
In view of this I believe treating any manmade rugs would be futile as the liquid would just run off the pile fibres. Wool rugs don't need treating as wool is naturally retardent. Therefore they are only suitable for manmade and natural fabrics. In manmade fabrics the salts are trapped within the weave.