One surprising thing is that immediately after the first two US-gulf wars began, professionals came in a dug down 10 meters at archeological sites, and reportedly over 100k artifacts were looted. However, I just checked Google's AI and it initially refuses to agree with this even though those numbers were reported by the scholars in their reports. If you challenge Google's AI (I haven't tried the others), it will eventually agree but will still be really vague about it.
The recovery of the dead sea scrolls is also interesting. They 'appeared' in caves in Qumran, but many early reports suspected they were placed there. Also interesting is the character "Kando" who ended up trading them.
Given recent current events (I won't mention names to avoid my comment being downvoted out of the search history), we know there are a lot of powerful people who are into the occult and ancient rituals. So, I suspect a lot of the artifacts end up with them. Who knows.