When the Chief and Cortona land on the Didact's ship and realise the only option is 'plan B', Cortana inserts herself into the ship's system to fight the ship's security and help the Chief. From this point on she's now part of the Didact's ship. A long fight through the ship ensues until the inevitable final confrontation where Cortana helps the Chief defeat the Didact, who falls into the slipspace rift - fate unknown.
The Chief then activates the bomb which destroys the Didact's ship where Cortana is. It then transpires that Cortana held a little of herself back to exfil the Chief after detonation but before the actual explosion which is how he survived. She then tells him: "
I'm not coming with you this time. Most of me is down there" referring to the destroyed ship. You then see Chief floating in space among the wreckage where it's quite clear, the ship is destroyed - there are only small pieces of debris left.
If it wasn't any clearer, before they board the Broadsword for the Didact's ship Cortana says: "
They'll pair you with another AI. Maybe even another Cortana model if Halsey lets them. -- It won't be me, you know that right?"
All that remains of Cortana was a minuscule fragment that is suffering extreme rampancy. You have to consider that the UNSC don't value AI constructs, only their strategic knowledge. The reason Keyes entrusted Cortana to the Chief in the original Halo wasn't to protect Cortana as much as it was to keep her knowledge of the UNSC's battle plans from the Covenant.
There is no 'cure' for rampancy because the UNSC don't need to cure an AI, they just replace it. Any contrived explanation for trying to rebuild her would be utter nonsense and inconsistent. But this is 343 not Bungie
