She is alive. Sorta.
I still haven't figured out what kind of "thing" is that at the end of Halo 4 in which Cortana saved John from the explosion...but surely it's gonna be something Forerunner, like some sort of Domain. Thus Chief will have to go find her in a Forerunner Structure (I hope it being the Ark although is improbable) or he'll have to find the Didact to seek for answers.
Or she is integrated with some Ancillas, to form a Gravemind or something alike. But that's highly improbable.
