Could Cortana come back in the next games ?

The answer is yes, she could come back in the future games and hopefully will! I was demoralized when i saw that she faded away into death. However their are more likely outcomes that could resurrect her back into the normal Cortana that we love.

Lets start with these options.

1. When the ship fell into complete destruction with Cortana's AI brain pattern, we all thought there was nothing to come back from. However we do not know the extent of Forerunner ship technology. With the destruction at it's final stages the ship could have sent all of its data including Cortana to an installation which the Master Chief will possibly encounter in Halo 5 or Halo 6. This is the most likely explanation for the return of this much loved character.

2. (BEST) Cortana during the end scene in which she fades away touches the Master Chief physically. This could mean without her knowing (due to rampancy on her knowledge data banks) is stored into the Chiefs Suit. By doing this it would take her time to regrain her strengh inside the chief and unable to notify him. Which on that note would make a great game scene about the master chief on his knees in mortal peril and an enemy boasting "You are all alone, Your death is at my hand" or some other boastful line where Cortana (Who has regained her strengh) say's to the chief  "GET UP JOHN". The death of Cortana effects him hard, effecting his combat ability. With the resurgence of Cortana the Chief gets back into action.

I hope that this example is implemented into Halo 5 or Halo 6 and i hope the developers at 343 can go for one of these examples, instead of the one i propose next.

3. The recreation of Cortana from Halsey, with the death of Cortana Halsey began recreating another copy exactly in general for the Master Chief however without the memories. This would be the worst case scenario as everything you have fought for with Cortana would be meaningless, if only to create another copy to start over. Even though this would show that the Chief would get used to this Cortana.2 like the original Cortana and eventually bond. Although this would show the chief accepting the new Cortana.2 as a companion and rejection of her ever being the same cortana. this would still be the worst case scenario as a complete new copy without the individual aspects and memories of the normal much loved Cortana would just ruin the character altogether creating a negative effect around the story.

Another last option.

4. Salvage teams work exhaustively to recover Forerunner technology within the wreckage of the Didacts ship only to find most of the computer core intact with Cortanna inside. Cortanna salvaged out of the computer by Halsey is then reinstated to full operations (No rampancy). Return of Cortanna to the Master Chief is in route.

Cortanna's Rampancy for all of these examples could be cured by either the Forerunner computer core which automatically fixes and updates it's software and programs for the Didact's ship. Or by Halsey getting to Cortana first and repairing her neural net by the cloning of her brain.

These are all great examples to follow from and i hope that the 343 industries team decides to bring Cortana back into the fight, without being another copy.