I don't think it's common to find a Retained Fiber Strike Through on a proof coin. There is only one fiber retained. The other marks are incused into the surface with no fiber in them. Not the best photos, taken through plastic...
I'm not familiar with that coin. Where did you get it? I worked on a project connected to the James Webb Space Telescope at GSFC in Greenbelt, MD.
I see this is a new (2020) coin. It seems odd for a coin to not have a date. (laser frosting is terrible...imo)
Yes I know it's a strike through just never head of this type of material struck in to a coin and I'm guessing it only occurs on modern proofs.
It can occur on any type of coin metal, not just modern proofs. Images of strikethroughs from fabric have been posted here in the past. Canvas bags, too! I had some 2005 CA SQ business strikes in which fabric had been impressed on John Muir's pants leg. All it takes is one little fiber.