They could play it as you actually being a survivor of a zombie apocalypse. What I mean here is that you have to barricade yourselves in safe houses, go out and try to find needed supplies, and basically just survive.
Could play out a bit like this. You're trapped in 'big arse city' which is currently overrun with the undead, curiously enough though, they're only really active during the night. So, with this game we have a set day/night cycle and a sandbox type of world going on already. Now then, you need to make it to the other side of the city to an evac point. The catch is that you won't be able to make it in just one day, and you're still going to need food and everything else to make it, so you'll scavenge during the day and try to find a safe place to hole up at night. During the course of the game you'll meet other survivors that you can more or less recruit, some have special abilities to be able to make things for you, some help scavenge, some will actually join you on hunts, etc. Throughout the whole thing you'll be given a choice of moving your base or to just fortify the hell out of your starting one, even if it does end up being very cramped. You'll also have the option to spread out your survivors to multiple bases, or clump them up, or if you're a jerk, clump them up and make them zombie bait while you sneak towards safety. There's safety in numbers, but then the larger the group of people, the more zombies you'll have heading for them.