We do this frequently both on shelves on or benches.  We plainly mark the books as Museums Copies or Property of.........
We have not had any books go missing, and they definitely get used ( in fact there is nothing I like better than to see parents reading to their children).  Adults use them, too.  We often have adult resource books available in the galleries as well.
Occasionally a book wears out - e.g. a cover comes off or there is wear and tear.

Kathrine Schlageck
Beach Museum of Art
Kansas State University

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