This seems like a severe case of plot inconsistency... at first, but it might actually be completely intentional. The ending dialogue's purpose slipped by us, so this might have, too. Let's look at what Henry has to say about this.
This ending is unlocked by throwing away at least one of the Animatronics that the player finds out in the Back Alley during the Salvaging Period of each shift. At the end of the week, Cassette Man congratulates the player but then states that they did not meet their special obligations under Paragraph 4. And their employment is terminated.
The Insanity Ending results if you have the Egg Baby (Data Archive) item in the room. Once you placed the Egg Baby, you will need to go to the terminal. Turn off the monitor in the terminal, place your cursor on the button on the bottom left of the monitor and hold the left mouse button, then turn the monitor on to reveal secret blueprints. As the blueprints play, you learn from Cassette Man that the souls of the animatronics will never be at rest, and he needs to get them into one place in order to destroy them all. After you witness that, the ending cartoon is shown. It reprimands you for "looking where you shouldn't have", and says you shouldn't have seen that. The narrator then presents you with the Certificate of Insanity, so that no one will believe you if you decide to tell what you have seen. The last shot of the ending shown you being taken somewhere for brain lobotomy.
This is the part where one of the most recognizable FNAF moments took place when he had his speech for all present animatronics. He left a special message for everyone captured, and the most touching one being the message for his daughter.
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