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Shinjo said that Kagerou's AI chip was wiped before it was put in the submarine but despite that, at the end, Kagerou came through and activated the escape pod for Shadowmaru. So!
Later in the series we see that Super AI chips can reject reformatting - Deckerd's subconscious cut all access to his memories even after he agreed to the process in the first place. I have no doubt that Kagerou's AI wouldn't be any different - especially when he was about to be wiped against his will and earlier made it very clear how important the memories were to him. However, unlike Regina, Shinjo didn't have a spare chip at hand and if he wanted to make his plan work, he had to find another way.
I believe that Kagerou's data was simply partitioned away, encrypted, and Shinjo's data added on top. That's how Kagerou was able to break through just a little at the end, because he was still there, trapped and locked away, talking to Shadowmaru through a crack in the concrete wall he was put behind.
And then, in the golden glow of the sunset, Shadowmaru sat at the pier, head down, palm curled in a fist. The team tried to console him, only for Shadowmaru to open his palm... with Kagerou's AI chip in hand.
Shinjo's speech about Kagerou being wiped was nothing more than arrogant boasting to add salt to the wound. And with the right tools, enough time and patience, encrypted files can be recovered.