This is a crazy idea I came up with for Johnson to still be alive. My theory is that after the events of halo 3 somehow his conscience is transferred into the damaged 343 guilty spark by some 4 runner creation.
I have no evidence to back this up, its just a crazy idea I came up with.
Sadly, it’s just possible given what we know about such matters. 343 Guilty Spark (Chakas) did survive and he’d have mentioned retaining Johnson’s personality or consciousnesses back in Halo: Primordium. Even the Composer wouldn’t work as you can’t transfer the consciousness of anybody who is dead. And, of course, there was no recorded Composer on the Ark or on Installation 08.