Styrene shades are a firm fabric covered material. They are A-frames or drums that have a wide range of sizes. The drums often have a spider top wire that drops deep into the shade. I have seen cut corner shades that were also done in this material.
These shades were made very specific in size and trimmed to match the lamp base. I very patiently remove the delicate trims to re-apply to the new cover in the same location as the original shade. These trims are remnants of our lighting history.
The nice thing about this technique is almost any material/fabric can be used to adhere to the styrene. I have used suede that made a beautiful finish.
It is surprising what people will hold onto until they find someone to help.