What are we looking at, here? I am weak, I need context.
It appears to be a padded cell that has seen better days.
Do they usually use velvet on padded ceilings? That pale green stuff on the right of the image seems to be velvet that's seen better days.
That's shadow. You can tell because it continues, with a break for depth, into the metal piece under the insulation.
What you're seeing that appears to be a velvet nap is actually the wear pattern that results when you pull or strain synthetic duck-type (basket weave, or at least multiple-fiber per strand in the warp and weft) fabric. The light catches on the synthetic fibers and makes it appear satiny, which can also look like velvet. (Satin is in fact when you have long weft threads that jump over multiple warp threads, so the effect is similar.) This looks a little like nylon, but could also be fiberglass or kevlar. Based on the fact that it's torn though, I'm going to go with nylon, which was not very smart of someone - clearly.
Looks like industrial insulation over corrigated metal. Also looks like it wasn't blown properly and then the covering deteriorated.
I'm going to guess that it's the insulation on an HVAC duct, chewed away by some rodent.
Given the headline I'm guessing a tour that included a long-disused padded cell.
The exif data places it at:
This is in the back room of a collection agency? Yikes!
There's also a "Location" link right up there in the post, Encyclopedia Brown.
Newton J Tharp. City Architect. Google for interesting facts.....yada, yada, etc.