speaker cable that would work under a rug

There is a company called "the cable Company. https://www.thecableco.com/

They have an excellent selection of all sorts of cables. I have had good luck with the Goertz cables. They are specifically designed as being flat, as in wafer thin flat. I believe if I remember correctly you buy by the foot. Good luck. 

@mcanaday 

I would never run cable under a rug. If you have continuous wall down one side of the room (no doors), I would get a heavy gauge pair of speaker cables and run them from your amp along that wall to your speakers. Any excess cable can be loosely coiled behind the first speaker in the run. I have thirty feet or nine meters of Kimber Kable 12TC in my room. Though the capacitance is rather high for each leg the total run at around 4400pf, using any kind of ribbon cable is significantly going to exceed that. There are some amplifiers of somewhat questionable design that would be adversely affected by that, probably an OTL and some direct coupled solid state but that is rare these days. Amps with output or auto transformers are especially immune because they protect the output devices from the effects of the load to a great extent.

Nordost. We've had it inder our home theater rug for 21 years. Very tough flat cable.

I love my Anti Cables flex, they sound amazing, won't totally bankrupt you, and they can easily go under a rug. They are stiff, but once you bend them into place they won't move. I was able to get them to go through my speaker stands which you will never do with more big thick cables.

They have amazing bass, totally liquid smooth mids, highly recommend their speaker cables, but the rest of cables are Acoustic Zen and Acoustic Revive.

Parts Express still sells the Audtek braided speaker cable that is flat, and meant for exactly this purpose.