They were looted. The tomb of Cyrus, in Pasargadae, was looted even in antiquity. According to Arrian, when Alexander visited the tomb, he found it looted and mostly empty, and was furious. There had originally been a golden coffin, rich textiles, et cetera. This event probably impacted upon the young Alexander and his close associates greatly. If his great tomb is still out there somewhere, hidden, it is very likely that the sight of the looted tomb of Cyrus had a lot to do with it.

Virtually all ancient tombs that were not hidden or protected were looted in antiquity. Those that somehow survived were looted in the intervening 2+ millennia. The mausolea of Augustus and Hadrian, for instance. Nothing can survive the ravages of human greed and destruction, except by accident. In the pre-modern and modern periods, professional looters became adept at finding even the hidden ones. They scoured the countrysides of Europe and Asia, sensitive to the subtle signs. In Italy, thousands of Etruscan tombs were discovered and looted this way. The great museums of the world (the Vatican, the Louvre, the Met, the Getty Villa, e.g.) are stuffed with illicitly-acquired antiquities pulled out of the ground in the middle of the night by professional looter gangs. Modern anti-looting laws and better awareness and enforcement have stopped the flood somewhat, but the majority of the damage had already been done before the 20th century. The high-profile, rich, Western culprits (like Elgin) are easy to identify and make easy targets, but far more damage was done by local gangs who were in abject poverty and had nothing to lose. In the 21st century, strict antiquity laws have backfired in many cases. In Greece, we hear about farmers deliberately plowing over and destroying Mycenaean sites because they think that reporting the find would cause the government or the EU to seize their land.