I wish I had a good source, but from what I've seen firsthand (well, by following the Japanese car community and having friends in it) there's a pretty large export market for stolen cars. Either the full car is exported or people literally chop off things like front bumpers for popular cars, remove special limited parts, etc. There's probably some Japanese car website with actual numbers, but it can be unnerving whe…
Doesn't Japan also require you to junk your car after two years or pay an arm and a leg for a yearly pollution inspection? If that's true, that's probably a much bigger stream of profitably exportable cars than theft.
The car is exempt for the first few years, then gets checked yearly. Most cars pass with few, if any, repairs.