From my understanding, MOST of Cortana was inside the Didact's ship's systems. When MC detonated the nuke he destroyed the ship, along with whatever part/s of Cortana that were integrated. I don't know how she made the "shield" for MC (something with the hardlight technology).
The Librarian is also physically deceased but left a program of herself behind.
I'm sure Cortana will return. I dunno how but she has to.