When your school library is chock full of selections, and teachers do not have a check-out limit, you don't really need to stock a classroom library. Page also allows children with fines to borrow leveled books, since those are purchased with grade level funds. Basically, there's no excuse for being without a something to read.
But...if you have piles and piles of paperbacks, why not turn them into a cache of reading material for your classroom? There's probably a store near you that allows you to do just that. Familiarize yourself with the business first. There might be a minimal fee for considering the books for trade. This is a fee that you pay even if some of your books are turned away. Determine how much credit that you get based on the book's cover price and the store's posted policy. Is that credit limited to the same genre? For example, say your grandmother donates all of her Harlequin Romance novels to you. Will you only be able to choose books of the same genre? Not exactly what you had in mind for your classroom, is it?
Once you've decided to gather up gently used paperbacks, tell your friends and family. Maybe they want to donate a portion of their hoard to your cause. If people have given books to your classroom that are not popular with your grade level, turn them in and switch them out. They'll understand.
I just cleaned the shelves of all of the good young adult literature in a certain Newport News shop, so you may want to try another spot for now.
Or is it time for you to power up with some books that have nothing to do with your classroom? There's nothing wrong with that.
One more thing before I go, what's with that kid that has library fines all year long? I mean, you take your students every two weeks just so that doesn't happen, right? Psssst...if your library doesn't allow kids with fines to take a book home with them, I'd be willing to bet that kid does not want to read. Don't let cash stand in the way of quite-possibly-the-best-book-ever. Make a plan to block all of his/her attempts to avoid reading early. Build in some success with the most irresistible books you know.