If you're in the UK, next-time you're forced to do a cull, try to see if you can find (or just start) a Bookcycle/Shelfcycle nearby. There aren't many yet but they're growing. It's a charity explicitly designed to do a better job of valuing donated books than existing infrastructure. They worked out that places like schools in developing worlds can often make great use of the books that other charity shops would destroy because they don't sell quickly in UK charity book shops. So Bookcycle sells the ones that would to raise funds to send the ones that wouldn't as a donation to communities that would value them. They try really hard not to destroy any book that someone might still find value in somewhere.