Mira Hnatyshyn asks:
I’ve read that museums keep copies of some of the paintings, for example Starry Night by Van Gogh, on their walls while sending on exhibition tour the original. Is this true? Or Visa versa?
Thanks for your question, Mira. LACMA has never replaced a work of art with a replica while the actual piece is traveling, and the same is probably true for most museums. The closest we’ve come—and something which is common practice—is to hang a small photograph in place of the work with a note that says the original is on loan.
Nancy Thomas, Deputy Director
Unframed The LACMA Blog 
Actually, the Musée des Antiquités Nationales in Saint Germain-en-Laye (FR) exhibits a replica of the Venus de Brassempouy (the original is deemed too fragile for display and is kept in storage) and a fac-simile of the Lascault paintings (original cave is closed to the public). And in contemporary art the practice of building exhibition copies is pretty common. Jeff Wall’s Dead Troops Talk exhibited at the “Face à l’Histoire” show at the Pompidou Center in 1996 was an exhibition copy, also many Smithson’s installations tend to be partially or entirely reconstructed works. Same with every retrospective of Kurt Schiwtters where modern-day reconstructions of the famed Merzbau are always shown.
While this doesn’t mean that “museum put copies on the wall while the original work travels”, the practice of exhibiting replicas/copies or fac-simile of works too fragile to be exhibited or that are no longer extant is fairly common in museums.