Does removing rfid tags from library books allow for theft?

Hi, I work at my school library and we are currently having a problem with stolen library books. We are wondering how this is happening, as there is only one entrance/exit to the library and no one has noticed kids holding books above their heads as they walk out. One thing we are wondering is whether kids are removing the RFID tags from our books and leaving them somewhere in library, then simply walking out with the book in a bag. Is this possible? If not, what could be the explanation for our problem?