There’s conductive thread and fabric, but have you heard about conductive hook and loop fasteners? I’m not exactly sure what you’d use it for other than Electrostatic and RF shielding. Maybe you could use it as a switch for some project, or to detect if the last guy through the dust barrier actually sealed it behind him.
The one inch-wide strips will conduct electricity both along the length and from the hook side to the loop side. When closed the resistance across the fastener is 0.8 Ohms. Expected to last 5000 opening/closing cycles, the silver-coated fasteners can be either sewn in or glued.
The stuff is not cheap — it runs about $17 a linear foot. That foot will cost $7 to ship and every additional foot adds around another $1.