What highfigh said. If there is a third bare wire in the 22 ga. cable, that means the cable is shielded and it can be used as a signal cable, if you solder RCAs to it. Alternately, you might be able to fine some kind of RCA wall plate that will accept bare wires on the back side, and you could just use a pre-terminated cable between the wall and sub.
Regards,
Wayne A. Pflughaupt