What you are asking for is called a flexolator.

Actually flexolator is the foundation spring/cage found on a lot of modern truck seats. I believe he is talking about burlap with wires embedded in it. This was put on top of springs to keep individual springs from collapsing. You find it used a lot on Chrysler products. I believe Legendary AutoInteriors carries it.

There is a similar product used in commercial furniture manufacturing. I've seen it used as spring cover on restaurant booths. The wire is embedded in the material every inch or so, but the material is not burlap. It's a synthetic material like Typar. I've tried searching for it with no luck, but somebody is making it for commercial seating makers.

I checked a few of my catalogs from different suppliers and did not find it. I suppose maybe I could call Legendary, because I did not see it in theirs.
Yes I am looking for the burlap with the wires in it. Customer wants original but not the old wires as he had mice and was worried they might smell urine on the old wires if I wove them into new burlap.

Ive seen the typar material that Jim mentioned on car seats as well.

If it's not available as original, some guys will take the time to make it. Get some thin, hardened wire (peel the paper off paper wrapped wire if you have to) and weave it every 1-1/2" or so. Tell your customer how much it's going to cost him, and he might not think he wants it so badly.

Fred Mattson can pitch in on this. He takes the time to painstakingly reproduce obsolete parts. He can tell you how he proposes it to customers.