The Didact is now an AI, similar to Chakas/Guilty Spark.
Cortana either dies or uses the Composer to take on physical form (an understandable choice for a Rampant AI in the final Jealous stage.)
The Didact uses the Composer to share minds with Chief, like how the ancient human general guy in Primordium shared spaces with Chakas and could sometimes take over his body.
To support my last prediction- in the Halo 4 gameplay trailer, Chief is collapsed on the floor under an orange glow, as he forms a fist while the Didact says “I have waited a long time for this, Reclaimer.”
Some people have thought that this was the Didact’s fist, assuming he has only been in cryo or something, but pausing the frame shows that this is the Chief’s hand: green armor, and index finger missing armoring for the trigger.