I know someone who once trapped a cockroach in a box and sealed it shut. When the box was opened, years later, the roach was still alive. It had eaten some glue on the inside of the box, and then went into a kind of torpor, simply waiting for either death by dehydration or starvation or an opportunity to escape, whichever came first.
Zombies are like that. They gorge on fatty foods, like brains, bone marrow, and body fat, then go into an induced stasis that outwardly resembles death.
The zombinism vector is undoubtedly an endoparasitic fungus related to Cordyceps. Mycelium spreads throughout the host during the infection, preferentially following existing neural pathways, and flooding the body with antibiotics, to kill native gut bacteria and other possible putrefying factors. The normal digestive functions are destroyed. The regular circulatory system is destroyed. The only elements preserved are sensory organs, muscles, skin, and bones. All other functions are replaced by the fungus. The mycelium, as it followed the existing neurons, actually grows into a replacement brain and nervous system as it destroys the host's nervous system.
The copy isn't perfect, though, and genetically hardcoded structures produce an instinctual desire to seek out and eat more fat. Destroying the head does not actually kill the fungus, but it does remove its ability to create a facsimile of a mammalian brain, by scrambling the template. It could still make the muscles twitch, but would have no means of coordinating them into coherent movements.
I would therefore expect a zombie running low on energy to have almost no fat left, and ascocarps growing out of it all over, like cactus spines. It would probably resemble a spiky mummy. Any rotting appearance would be due to colonies of microorganisms that have evolved resistance to the fungal antibiotics.
So it's not just eating brains, but also not spending as much energy as a human normally does while using the organs evolved to keep a human brain alive.