Zombies - Part IV

Didn't you ever wonder when watching the zombie movies what would happen if everyone died? I mean, the zombies feed off the brains of the other people. If everyone died, and all living things became undead, except for those that are now the dead undead, and those people less fortunate to not become undead, do the zombies just starve to death? Are they doomed to walk the earth in search of brains that aren't there? I want answers! Somebody get George Romero on the phone!