Old bows only last so long, after all-- why not make a bit of quick cash getting rid of your old one?
They may be refurbished and put back on the market, brand new, or they may be recycled and used for some interesting craft.. you never know!
Either way, I'm looking to pay premium for them. Perhaps even a thousand yen for a bow in unusable condition!
Visit the old tavern on the far west edge of the human village on Wednesday evenings or nights, and ask for Juhou Nene.