Is that exceedingly rare? I am surprised, I would assume the Japanese equivalent of a green card would be highly sought after for much the same reasons
A person with no Japanese ancestry becoming a citizen is exceedingly rare. It does happen, but not very often, and the process is onerous.
Applying for PR is more common, but still a burdensome procedure and is ostensibly only granted to those who either have a direct connection to Japanese family, either through ancestry or marriage (especially marriage resulting in procreation), or who have achieved some kind of major conventionally recognized accomplishment (e.g., winning the Nobel Prize):
If a child would otherwise be stateless, then they will acquire Japanese citizenship if they are born in Japan. But since Korea has a similar system, Korean children aren't stateless, they are Koreans.