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 is 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 has entered Purgatory and returned was Merlin's father. After a single minute in this dimension, her father returned looking like 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 suggests 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 on the brink of insanity. The land 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 continuously 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.

Meliodas wakes up and sees Ban to whom he believes is a hallucination but upon realizing he is the real Ban, cries over him, believing he was never going to see him, Elizabeth, or the others ever again. He explains how the Demon King had him imprisoned to make sure he would not get back to his body and eventually turned into the dragon after being consumed by rage and the Demon King decided it was okay to let him go since he could keep the exit with him to make sure Meliodas would not find it by chance.

The two of them find and kill a naturally-born creature of Purgatory that has a physical form and use its remains to create weapons and new clothing that can resist the atmosphere, and begin their search for the exit to the real world but during their voyage they are ambushed by a stranger who says he is curious how Meliodas and Ban are looking for an exit. Meliodas asks them if they know where the Demon King and the exit are, to which he agrees and says he'll show them if they take him with them, showing he is a pig who looks just like Hawk who is named Wild, he is searching for his long-lost younger brother.

Wild leads Meliodas and Ban to his house as a hot sandstorm rolls in, and they find out that Hawk, then named Mild, was originally born in Purgatory, and the Demon King sent him to the outside world 8 million years ago. Meliodas surmises that a minute in the outside world is equivalent to a year in Purgatory, making Hawk's appearance in Britannia 16 years ago plausible. The reason as to why Hawk was sent was to make sure that a sturdy creature was able to watch Meliodas' actions in the outside world for the Demon King, as opposed to the animals of the real world that the Demon King originally used, who ended up dying quickly. Meliodas and Ban share stories about Hawk with Wild, and Wild accepts his brother despite how different Wild expected him to be.

The trio resume their search for the Demon King once the storm blows over, and Meliodas tells Ban and Wild about how Zeldris became the demon he currently is but when prompted to talk about his other brother, Meliodas realizes that he cannot remember anything about Estarossa. The Demon King arrives, saying that Meliodas, just like him, is unable to remember anything on his second son. Disgusted by the effeminate nature of Meliodas' emotions, the Demon King looms threateningly over the trio and questions on how Meliodas's emotions returned to his original form and why he and Ban got there, the Demon King quickly realized that Wild guided them to the door to the other side. Wild bravely charged at him, saying that he will finally force through the Demon King alongside Ban and Meliodas, but the King effortlessly flicked him away. The Demon King then began pressuring Meliodas and Ban with his sword attacks, declaring that they will never return to the living world and soon cutting off Ban's arm. After commenting on the Demon King's massive power, Ban attempted to steal the King's power but the Demon King's Magic Power repels the assault back to Ban, instead absorbing Ban's power for himself. He continued attacking with his sword while laughing mockingly at Ban and Meliodas for their efforts. The Demon King is soon attacked by Wild but remaining completely unfazed, he simply grabbed and threw him away while admonishing them for not giving up, confidently saying that as long as he guards the door, it is impossible for anyone to pass through the door. Not fazed by Meliodas's comments that he is not the one who decides that, the Demon King simply corrects his son that he is the one who decides everything in Purgatory and unleashes several strikes of thunder at Meliodas but Meliodas Full Counters it. Remaining unfazed by it, having absorbed it with his magic power, the Demon King gives them the choice of continuing to fight and be killed or to flee, but he suddenly asks on what Meliodas knows on Estarossa, as he cannot remember him while he remembers all that happened as well as every member of the Demon Clan. When Meliodas tells him that while Estarossa was his son, he was born without the power of darkness and a weak-hearted coward who couldn't even kill a single insect, the Demon King completes that part by saying that he took pity on him and gave him a Commandment, shocking Meliodas. The Demon King then realizes that Gowther is behind this as he was the only Commandment who betrayed the King and the only one who can do so.

Inhabitants
In Purgatory there are two kinds of creatures:
 * Foreign species: These are the souls fallen in Purgatory that transformed by rage into pitch-black creatures with no definite form or substance. When they die they turn to dust.
 * Indigenous species: These are creatures naturally born in Purgatory, with evolved bodies that withstand the extreme conditions of Purgatory. As they have "substance", when they die they leave corpses, that can be used as a source for materials to make cloths and weapons.

Trivia

 * 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. Unlike the Capital of the Dead, which rejects the living, it seems that both living and dead can co-exist within the latter.