Though I am not a fan of undead in Mutant Future, or Gamma World for that matter, I do believe there is a place for spirits and even a spirit world. These are not undead beings, but rather AIs, including uploaded minds. A few uploads still have their brain tissue and are stuck in jars. The great majority of spirits are trapped in their machines but a few have the technology to escape by switching minds with a biological creature, android or robot.

The spirit world is virtual reality. Considering the state of the physical world, much of it is either horrific or paradises meant to shield the sanity of the spirits. Physical people interact with it via VR gear. All such gear protect the physical body of the user (even if the power goes out or there is a surge), but sanity is another thing. It is also one way for spirits to replace minds in the physical world. Still, the amount of useful information in the remaining servers is enough to draw people (usually shamans) into its cluches. Those within it have to learn the rules of the programs- the laws of physics may be very different in there...

A few mechanical benefits from entering the spirit world and finding the correct information include battle training with artifacts (up to +50% technology rolls as well as improvements to attack rolls and armor class), instruction on medicine and manufacturing and bonus languages. Contact with far off allies, maps (obviously way out of date) and access codes for vaults are also wealth that can be found in the spirit world.

Spirits and the spirit world allow for access to the old world but such hazards it isn't a simple "push button, get riches" process. The PCs may find themselves spending decades of subjective time trying to track down something vital to save their people (and it only takes a few minutes of real time).

Adding a spirit world to your setting adds another layer, one that could make Mutant Future all the more interesting for you and your players.