I think that CEO corps are immune even to nukes, but of course the loss of population will have virtually the same effect.
Feel free to correct me if I am wrong. A game message may say that it will close, but it may not actually do so. I got fooled by this once in a natural disaster. I took out all supplies out of it, and the money (when you could take money out of indivdual corps), and it didn't close. It bought new supplies, took out loans to do so, and it was a big fat mess.