This is also from the Osaka Information Service, that great service for non Japanese living in Osaka Prefecture... like me. I found this when trying to figure out what documents were necessary to change the address on my registration card.
Question:What about the alien registration of illegal residents?
Answer:Illegal residents are also required by law to complete alien registration. In the "Status of Residence" column of such resident's registration card will be written "None". Illegal residents are required to renew their registration every year.
Yeah. Cuz that makes sense.
Just as much as illegal immigrants paying taxes in the States.