A Festering Corpse is one of the different variants of Zombies. These zombies died and turned long ago, evidence of this being the fact that their bodies are highly decomposed. Although they're still walking in search of humans to kill. They share the same model as the Crawler Zombie.
One headshot with a 100% condition Pistol is enough to kill it. It may be slightly harder than usual to score a headshot on this zombie due to its shambling walking pattern, especially with long-range Crossbow headshots.
During night, the running behaviour is standard as all other zombies. If distance or sheer zombie numbers aren't a concern, scoring a headshot when it's running headfirst towards you can be slightly easier.