I expect it varies depending on the store, but a place near me has things like remnants and ends of rolls, upholstery fabric sample books, offcuts of things like leather (the bits left around the edges after the pieces are cut out) and the ends of elastic and lace rolls that are too small for manufacturers to be bothered with but perfect for home use.

Not sure about all of these, but Upcycle Creative Reuse in Washington, DC takes donations. I’ve gotten some good deals there. A lot of the fabric and notions are unused from personal stashes or business overstock. They also have a ton of general crafting supplies.