Hellhounds are a special type of supernatural creature, hellhounds possess the bodies of those who already died.
The best example in the series is Jordan Parrish. Parrish doesn't actually know he's a hellhound for a long time, but his body carries out its duties of protecting the supernatural. Like another supernatural being, hellhounds can sense death coming. They also work to protect supernatural elements from discovery by destroying any evidence that they existed. Unlike most supernatural creatures, they can pass through mountain ash barriers, and they heal much more quickly from serious wounds.
