A shop or gallery would always be legally responsible for taking good care of works it received on consignment from artists, and should make careful arrangements accordingly.
When the shop/gallery negotiates its deal with exhibiting artists, there should be a discussion about insurance; and whatever is agreed should be recorded in the written exhibition contract.
In the unlikely event that an artist agreed to take out insurance instead of the gallery doing so, the shop or gallery would still be legally responsible for any damage to or loss or destruction of that artist’s work; and if that artist made an insurance claim for financial compensation, the artist’s insurers would not pay out before it had first claimed the compensation from the gallery or shop.