I have my doubts this is really a case of Illusion throwing away an established brand just to restart as Illgames (I mean, sure, we all knows it's Illusion, but new customers moving forward won't). I've read some speculation that it was to get out of some sort of contractual agreement to make AA3, but that's not how contracts work; unless there was a really weird clause that allows Illusion to not pay the penalty for breaching the contract in the event they shut down (which no decent contract lawyer would write, that's literally asking to be scammed), the penalty would be listed as a debt they have to pay off as part of the winding-down process. Trying to shift assets from Illusion to Illgames in an attempt to dodge this would just result in a lawsuit.
Now this is going to be largely speculative on my part, so take what I say with a grain of salt, but if Yoshimura Tei was the sole proprietor of Illusion (I don't know how Japan's business registration lookup works, what I can find isn't telling me much at all), it's possible that he's retiring and it was cheaper and easier to simply "fire" everyone, pay the termination bonuses, and have the successor company rehire everyone, than it would've been to go through the process/fees/taxes of transferring ownership of the company and the company bank account to someone else.
Also have to keep in mind Illusion was founded 30 years ago, there have been a lot of business and banking regulation changes since the 90s (especially after the 2008 financial crisis); it could also be a case where Illusion no longer met current requirements, but was allowed to operate due to grandfathering exemptions (can't cancel or force all of the businesses to update at the same time, that'd piss off a lot of old business owners and swamp the government offices with paperwork), and when it came time to transfer ownership too many legal hurdles came up.