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The elixir of immortality was created by Eirin Yagokoro using Kaguya Houraisan's power over 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 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 Hourai Elixir are known only by Eirin Yagokoro, whose name points her out to be the "Mind of God", an omniscient being. Because she made the Hourai Elixir the true elixir of immortality, she probably also made it irreversible, making its effects perfectly permanent. In her confrontation with Mokou, Alice points out that the soul is made invincible. This, along with Yuyuko's and Yukari's scenario in Imperishable Night, makes it seem that the Hourai Elixir itself isn't a power that keeps one immortal, but makes one an existence completely independent of even the concept of reality, thus making one not subject to the bounds of life, death, or even manipulation, although the pain of injuries can still be felt. This medicine indeed makes one truly invincible, and forced to live out their existence forever. It's no wonder why this medicine is forbidden even to the mysterious lunarians.
Since this elixir is forbidden, and only Eirin is known to be capable of manufacturing it—and even then only with the help of Kaguya—it is understandably rare. Only three people are confirmed to have ever drunk it: Chang'e, Kaguya, and Fujiwara no Mokou. It's also possible that Eirin herself drank it, but it has never been confirmed. In the past, this elixir has been used by Lunarians to test influential humans or to cause disturbances on Earth. 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 Cage in Lunatic Runagate: Chapter 1, 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 Hourai 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 Fujiwara no Mokou's backstory in Cage in Lunatic Runagate: Chapter 4. There is no information as to where the Hourai Elixir is presently or even if there is any left.
Reportedly, the ingredients of the elixir remain in the liver of whoever 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.