Sigh. I'm going to break some hearts here, I know, but: Being a good librarian means getting rid of books which are no longer used. It's just a fact of life. We call it "weeding", and it has the same purpose as in gardening. We weed and discard books all the time.
And as I tooted a few weeks ago: Please don't donate your ratty, moldy books to us. We won't use them. We won't give them to our FOL. We'll just do what you wouldn't do: Throw them away.