Subwoofer: RCA from speaker wire

Put an RCA jack on either end of the speaker wire, done. RCA is just a 2 wire system, ground and signal, same as speaker wires, or a 2 prong electrical cord. It's jsut the ends.

Speaker wire will be fine, but make sure you are having lower input coming through and not 600 watts coming over that. You can put an rca plate over the speaker wire to make it easy.

Could you by chance pull the old speaker wire out and fish a coax line in its place? You can use rg6 coax for this application.
If there is any 90 degree spots in the pull (like say at an attic or crawlspace) that will require you to be at that location.
Wrap a piece of pulling twine (sold at lowes and home depot as well as online) very tightly around speaker wire 4-5 times and thoroughly tape it electric tape. Then pull speaker wire out (you will need to physically go to any location that has 90 degree bends to pull) and pull the speaker cable and twine through until you have removed the speaker wire and the twine goes from point A to B. I highly suggest one of these for pulling the coax through: http/www.techtoolsupply.com/ProductDetails.asp?ProductCode=85%2D901
Now push the coax at least half way into the device above and attach the cable/fishtailz to the twine by tying the twine very well to the loop on the fishtailz.
Now just slowly pull the twin from the other end to fish the coax back through the wall, as with the speaker wire you will need to manually pull and position the cable at any spot where it 90 degrees in attic or crawlspace.

Digital coax has 75 ohm impedance that your speaker wire will not provide well. While you can technically wire the speaker wire to a coax plug and use the - as the ground, it will not likely sound very good.

In regards to the wall plate I would need to see a picture. You may be able to just remove the banana plug and screw in an rca terminal on the plate, or you may have to widen or make your own hole for the rca plug.

What is an RCA jack? 2 pieces of wire with a plug on the end. What is speaker wire, 2 pieces of wire without an end. As long as the gauge is a good enough gauge, put an end on it and plug it in. It's not sending any watts or power, it's a powered sub, so the amp is only sending a line level signal.

People are over complicating this.

The simple solution given here by many posters (just put RCA jacks at both ends, plug and enjoy) will work. Only potential problem might be some interference caused from non-shielded, non-twisted long cable used for weak analog audio. If the output and input are low impedance (600 Ohm or less), interference will not be a problem i think.