Plenty of actual thieves just keep the artifacts for themselves, without damaging anything. British museums get a lot of hate for taking home artifacts from other countries.
An old caliphate might be the equivalent of the UK today, a seemingly invincible power, but after a few hundred years, it collapses and its treasures are looted by some other victor.
Maybe another example might be something like the True Cross or other religious relics. They may not be damaged, but it ain't archeology.
