Purgatory

Purgatory is the space between the living world and the afterlife.

Background
According to Merlin, the Purgatory is a place of chaos where mutilated souls and predatory monsters seek prey, how there's scorching heat, blistering cold and toxic air that destroys the flesh of the living and how time and space are warped, saying that a minute corresponds to a year in there.

At some point after the Holy War, the Demon King was imprisoned in the Purgatory.

The only being who enter the Purgatory and returns was Merlin's father. After a single minute in this dimension his father returned back looking as an old, invalid person.

Plot
After his defeat by the Ten Commandments, Meliodas does not move on to the Capital of the Dead but to Purgatory, instead. There, he confronts the shadowy remnants of the Demon King while waiting for his revival.

When Merlin discovers that Hawk was connected to Purgatory and that the Demon King had been observing them through Hawk's eyes, Diane suggest that they can go to Purgatory through Hawk in order to recover Meliodas's emotions that have been stolen by the Demon King. However, Merlin reveals that this would be an impossible task for them, but Ban affirms that he could make it since he is immortal. Skeptical, Merlin uses an enchantment to send Ban to Purgatory.

In Purgatory, Ban has been transformed into a pitch black fox-like monster fighting against other beasts, but manages to regain his sense of self. Ban's hair is extremely long, showing that he has been looking for Meliodas' emotions for decades, or possibly even centuries.

His flesh is constantly destroyed and recreated through Purgatory's atmosphere and his immortality is the only reason he lasted so long, but being always in the brink of insanity. The ground opens up and he skids down a huge chasm and splatters on the ground, before coming into contact with a dragon-like creature. He fights it continously for years on end and neither of them has fallen yet they both know their fight will continue forever at the rate they are going.

Ban reminiscences of the others waiting for them back in the living world, Elaine especially. He asks Meliodas to hurry and come back to them, but sees the dragon is gone. He hears a voice calling for Elizabeth and looks down to see the dragon was in fact Meliodas' emotions this entire time laying unconscious next to him.

Trivia

 * The Purgatory is presented as a counterpart to the Capital of the Dead; whereas the latter is a place where souls rest in peace, the Purgatory is more like a torturing prison to souls.