I made a bunch of collapsible wood stoves from flame-resistant fabrics about five years ago and posted just a couple of them here on BPL. I ordered all kinds of textiles in a huge variety of materials and tested them.
Organic (polymer) fabrics and films:
High temperature polymer fabrics and films (PBI, Kevlar, Nomex, Kapton film, etc.) can survive brief exposure to flames but don't come anywhere close to withstanding the temperatures at the bottom of a wood fire.
Glass and ceramic fabrics:
Fiberglass fabrics don't withstand direct contact with hot coals, so you can't build a wood fire right on top of them without something (like sand) in between. Standard fiberglass (E-glass) melts, and high-tenacity fiberglass (S-glass) becomes very brittle and eventually crumbles.
Vitreous pure silica textiles (Omnisil, Refrasil, and others) withstand higher temperatures than any type of fiberglass, but at wood fire temperatures it undergoes a transition to a brittle, crumbly, crystalline ("cristobalite") form. It also shrinks significantly.
Textiles made of Silica/Alumina fibers (not fibers of each type but fibers of a mixed Silica/Alumina ceramic) hold up much better than pure silica. They remain vitreous at high temperatures and don't become as brittle. Some of the "3M Nextel" fabrics are made of Silica/Alumina. Pure Alumina works also, but it's a little more brittle than Silica/Alumina. They are relatively expensive, and the lightest are in the 6 oz/yd range. These worked better for me than anything else.
Zirconia, hafnia, and other ceramics are made into woven fabrics, but most of them are much too brittle to be handled much. A company called Zircar sells a variety of these.
Ceramic fiber "kiln paper" is available, too, but it is consumable. It is held together with an acrylic binder that burns off, leaving a crumbly wafer of ceramic fibers. Nonwoven ceramic fiber blankets are available in a wide variety of materials, from low-cost "mineral wool" to pure alumina. These tend to be very heavy (20+ oz/yd) and they readily fuzz and come apart when handled or abraded, releasing clouds of fine ceramic fibers.
As others have observed, carbon fiber welding blankets are consumable. They are made of basically the same stuff as the coals at the bottom of a wood fire, so they eventually burn away.
Metal woven and knitted wire and foil:
Steel, nickel alloy, and titanium alloy woven wire products and foils withstand wood fire temperatures but are relatively heavy, bulky, and expensive. Fine woven titanium wire screens are available on Aliexpress for about $400 per square meter (minimum purchase one meter). I guess you could buy some and cut it into nine 12"x12" pieces and sell them on BPL for $50 each. Nickel alloy and steel screens are cheaper, but heavy.
Steel, nickel, and titanium foils are available, but I found that steel foils seemed to get holes and embrittlement. Nickel foils are heavy and expensive. Titanium foils work well, and there are lots of posts on BPL about using titanium foils for wood stoves.
In summary, I've only found two materials that can withstand prolonged direct exposure to a wood fire that are strong and lightweight: silica/alumina fabrics (3M Nextel materials) and titanium foil. Tightly woven titanium wire screens might work, too, but they're expensive. If you can protect the material from direct contact with hot coals with a layer of sand/loam/clay, you have more options.