Basically I Am Legend or Omega Man: The Game. I think near enough everyone has wanted a game like this at some point, even before zombies exploded in pop culture and got overdone. A real open world zombie survival game. Something like Day Z is probably the closest we have so far, but it's still in a pre-release state and offers a very specific type of experience, the general feel of it isn't exactly what I'd want.
I remember when Red Dead Redemption: Undead Nightmare was announced, while I did think zombies + cowboys was a good combo in its own right I was somewhat frustrated that they made a zombie expansion for RDR and not for GTA.
Honestly I think the closest thing is Fallout 4, in areas with ghouls, thanks to the survival options and the sheer amount of game mechanics. It's kind of versatile enough that you can mold it into your own game. There's also mods to swap out most if not all enemies with types of ghouls too, to turn it into a zombie apocalypse. Throw whatever survival settings you want on top of that and you have something that's not all the way there but basically close enough.
Last of Us is very close to what I'd want this to be, in tone, atmosphere and gameplay elements, but of course it's a linear game with no room for role playing.
I haven't paid much attention to it but Days Gone might be what you're looking for too. It's open world anyway.