speaker cable that would work under a rug

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.

Nordost has flat cables - though the run under the carpet would need to be pretty much a straight line.

Caution, lower end Nordost cables are possibly somewhat lean in sonic signature.

I have been running my Triode Wire Labs American Speaker Cables under my rug for the right speaker for almost 4 years now. It is a shag rug so that helps hiding it.

Just last week I ran it around the back of the speakers instead and elevated both cables to find out if I could hear a difference. I need to do more B2B but my initial impression is that I cannot.