While countries like Mongolia have the capacity to scower the earth for fossils lost to poachers and private collectors, the US forces museums to sell natural history heritage to the highest bidder. Illegal poaching is sad enough (often targeting the best and most scientifically valuable fossils), equally tragic is the legal business of the same caliber of fossils.
Examples of privately owned fossils, barred from science, includes a complete Spinosaurid skull, countless complete Oviraptorids, complete Allosaurids from the US, and a huge complete Rebbachisaur (very rare Sauropods) also from the US. They are all unidentified and unstudied, and will probably remain so.