An innovative way to reuse old or damaged books is to repurpose them for art. Having a wedding? You can create a “book arch” or make origami flowers out of book pages. Schools may also want them to create blackout poetry (where you blacken out words on a page, leaving only the words that create a poem). Check Pinterest for ideas.
If you have gently used books, enquire at your local library, school and church if they may be interested in them to sell at fundraisers or keep for their own collections.