My partner is the manager of a red cross shop here in the UK, and it's exactly this - anything not of resale quality (or just too 'personal', like used underwear) goes for 'rag' and they get paid by weight by the rag company. The rag clothes are shredded, IIRC, not sure what for.

They also have a book company who have a similar arrangement, they pay a few pence per book, though IIRC they do make use of the books as-is rather than shredding.