The Hourai Elixir (蓬莱の薬 Hourai no Kusuri) was created by Eirin Yagokoro using Kaguya Houraisan's power of the manipulation of eternity. Anyone who drinks this forbidden elixir will cease to age, never become ill, and will never be able to die. One will be as frail and vulnerable as before, but every injury shall cease; critical injuries will be healed in a matter of days. Complete destruction results in complete restoration.
The Hourai Elixir is permanent. According to Fujiwara no Mokou, the first taste of the medicine makes the drinker incapable of growing up or aging. The second taste makes them incapable of becoming ill. The third taste makes one completely immortal to the truest sense. The ingredients of the elixir are known only by Eirin Yagokoro, who is suggested to be Omoikane, a god of wisdom and intelligence. Reportedly, the ingredients of the elixir remain in the liver of whomever drinks it. Eating the raw liver of an immortal is said to grant the same immortality as drinking the elixir, though it will not deprive one from their own because they have already been rendered deathless.
Because Eirin made the elixir the true elixir of immortality, she probably also made it irreversible, making its effects perfectly permanent. In her confrontation with Mokou, Alice Margatroid points out that the soul is made invincible, forcing them to live out their existence forever. Immortality unties the soul from the physical body, which is just recreated as necessary, although the subject still retains all bodily sensations and functions. In this sense one is separated from the cycle of life and death.
In the past, this elixir has been used by Lunarians to test influential humans or to cause disturbances on Earth. Eirin notes that a Lunarian taking the elixir makes them impure due to being tempted by the removal of death and thus associating themselves with it. The backstory of the Hourai Elixir is that Eirin made the medicine on Kaguya's request to drink it, resulting in her exile from the Moon. According to the first chapter of Cage in Lunatic Runagate, Eirin felt guilt over Kaguya's exile, and when the time came to bring Kaguya back to the Moon, Eirin deceived the Moon's emissaries and fled back to the Earth with Kaguya. With this tied to the traditional story of Kaguya-hime, Kaguya apparently left the elixir to the old bamboo cutter who raised her and the emperor whose heart she'd stolen before she left to the Moon, resulting in Mokou's backstory in the fourth chapter of Cage in Lunatic Runagate. There is no information as to where the elixir is presently or even if there is any left.
Since this elixir is forbidden on the Moon, and only Eirin is known to be capable of manufacturing it, and even then only with the help of Kaguya Houraisan's manipulation of eternity, it is understandably rare. Only four people are confirmed to have ever drunk it: