I should have clarified - if one parent is Japanese, the country is a haven for international child abduction. If neither parent is, I'm sure the parent would be sent back to wherever he/she is from.

Also, this is a legitimate question from check-in staff - the airline will deny boarding to people who they suspect will not be admitted to the country (or allowed to leave - that happened to a coworker who forgot to renew her visa in Japan).