How about organizing a swap meet for people to get access to the textiles. One of the imperatives must be for the city to minimize its net expenses from this activity, so I would say the rules would be:

1) Any group can contribute its textiles, but they must be clean and usable (ie, not obviously ruined).
2) People can volunteer to remove zippers, etc as posted in another submission, but can only be paid in textiles.
3) Gather information about the best way to package textiles for use, and then bundle them together according to quality and kind
4) Sell them by the pound in wrapped bundles, with a description of what's contained in each one (assorted denim, very good condition, sizes ranging from 8x10inches to 32*32 inches).
5) If people don't want to use them after buying, they can resubmit them for portion of the fee paid.

I think this helps by getting the users to determine the quality of the fabrics themselves, and the city doesn't incur employee expenses.