In the United States, we have the opposite problem: Way too many aliens that the federal, state and county have no records of. They are preyed upon by criminals, and too many of them are criminals fleeing their home countries. I'm more attuned to the problems of illegal immigration since I ran into it working private security and interfacing with local law enforcement.
For Japan it looks like one problem is defining who or what a citizen of Japan is. To become a citizen of the U.S., you don't swear an oath to the U.S.; you swear an oath to support the Constitution. You also have to know enough English to understand U.S. history and laws. Perhaps Japan needs a legal definition of a Japanese citizen as opposed to a genetic one.
douglas chandler