Zombies eat. Let’s face it, that’s their primary goal. With all other forms of humanity stripped away they have one animalistic goal. To consume. In some cases they have been shown to be flesh eaters, and at other times, more selectively and bizarrely as brain eaters. I tend to lean towards the flesh eaters side of things. And considering their inability to think and reason (in most stories,) or at least their clouded and limited ability, it’s likely they would eat just about anything. A horse, a dog, a bird, or whatever happened to be around. Like predatory animals though, they are more likely to go after the best game, the living.
But what happens when they don’t feed? They waste away. All that rage and power, the relentless drive pushing them to get more food, the constant hunt, drains them. They aren’t solar powered perpetual motion machines. Eventually they run out of power. They wear out. And if pickings have been slim it gets harder and harder for them to hunt. They may take more damage in their more and more desperate attempts to feed. They could be very similar to the skeletals which are also last stage zombies. Wasters still have some chance to feed though and thus recover, though as food dwindles that chance also drops.