Japanese system doesn't have an open base of companies so Illusion's legal state is unknown. IPs don't become a public property.
I agree, I never said that KK / KKS become a public property in a legal sense, all I'm saying is, there's no legal entity left to sue you, therefore very likely free to take, noone will come after you (not that Illusion cared too much in the past TBH). This is in contrast to HC, which IP is owned by a very much alive IllGames.
... company must sell its assets to pay off its debts.
Again, I agree. That's why I think it is possible that Illumination have bought the VR Kanojo IP from them.
However, if a company decides to wrap up operations – for whatever reason – without filing for bankruptcy
While you're right we cannot know for sure, my understanding is, Illusion went down without a legal successor. Deliberately, to escape whatever legal baggage they were carrying.
It is also my understanding, that even though IllGames might be the same in every possible way (same people, same office, same desk, same equipment), they surely and definitely not the same in a legal sense; legally they are a totally new and independent entity.
here’s how IP rights are transferred based on the business structure:
Exactly. As I've said, the IP right never belonged to the employees in the first place. And again, I'm not a lawyer, but I'm certain that even in Japan, if an employee works in their clock time on the company's equipment, then that employee has absolutely no right to the finished product; that will entirely belong to the company who paid them. (Except if they have some sort of agreement, it's not without precedence to offer ownership or shares to employees, it's just not the default.)