The zombies of halo reachs gametype in custom and matchmakeing can have a logical explanation and here it is.
When the spartans died inside thier armor they were left in the armor to preserve the body sorta like a casket, they were either left on the ground in middle of a battle or taken to the morgue. One day someone or something uploaded a virus to the spartan armor in thier shutdown state which made the armor take on a life of its own with the dead body inside to keep it stable. So the spartan armor is like a exoskelaton, the virus bypassed the deceased spartans armors shutdown state bringing it to walk up and around. Its new goal is to destroy any electrical activity, scientist state that the armor is hunting down the electric activity in the brain and the activity in other spartans armor. The virus infected suits wont attack itself so any other armor that is infected with this computer virus wont be attacked. So when the spartans armor is brought up and about it will hunt and destroy anyboy who has electrical activity (which is basicaly any liveing thing with a BRAIN) and when it kills a spartan then the spartans suit will be infected as well sadly the spartan inside will just be a corpse with the armor bieing the actual one in control. The reason why the armor acts like a live spartan is because the suit still retained some un corrupt data on how to use armor abilitys and how to use few weapons. The energy swords most “undead” spartans use cant be explained much other than the suit find them or they make them with scrap. The spartan armor doesnt attack anything that is imobile with electrical energy is because they only seem to chase after mobile electrical charges hence a smart virus made by whoever or whatever made it.
Short version-The spartan inside the armor is dead, the suit is alive by itself.