A loose magic system based around salt.
Salt acts to preserve certain pathways in the mind that would naturally break down and be replaced. As more and more of these pathways form and are maintained through the salt, people will start manifesting psychic limbs that they can learn to control like learning how to manipulate their limbs as a child. By frequently using these limbs one strengthens them and can break human limitations of strength, speed, and endurance just by manifesting them.
However, the stronger these limbs are, the more salt buildup is needed to manifest them. And when one doesn't properly maintain these pathways, they rot and poison the mind, turing the salt wielder feral.
Salt men are the result of those whose minds were poisoned by improper maintenance of their powers. These zombie-like entities consume the salt in the living to power their extreme strength, speed, etc.
I'm also trying to make a reason for survivors to sometimes turn into salt men due to exposure to these energies flooding their system. They would essentially have to consume copious amounts of salt to not turn, making them targets to other salt men.