Permadeath is often a feature a lot of survival games are hesitant about, but I think it's a good option for those who want the added challenge of doing a 'perfect' run. That said, I think there's 2 good ways it could be implemented in the game.
1) Complete permadeath. When you're done with a run, you're done. finito. The save deletes and you start over, either on the same map or a different one.
2) Character permadeath. When you die, your character's done. You can spawn in a new character (Heck, maybe even force it to use a different character you've created?) and have to level up again but your old character's stuff is still out there in the world, if you can find it. Of course, depending on the gamestage your old character was at, their stuff might have degraded a bit and/or zombies might have infested their base, making reclaiming it anything other than a walk in the park.....
Personally I like the idea of my survivor dying, his stuff getting scattered around, and stumbling across it as I survive the area he died in. Or travelling to my former base only to find it overrun with cobwebs and zombies - lots of useful loot, equipment, and amenities if I can deal with the ferals inside. That sort of thing. Would make for a fun system where death simply means passing the torch to someone new, that kind of thing.