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 sick, and will not remain dead no matter how many times one is killed. One will be as vulnerable to damage as before, but will regenerate from any injury; critical injuries will be healed in a matter of days. Complete destruction results in complete restoration.
The Hourai Elixir is permanent. When tasted, one will be rendered forever and independent of the Hourai Elixir itself. With just one taste, the consumer is rendered ageless. With a second, the burden of sickness, illness, and disease is lifted, and one can never again experience them. With a third taste, the very concept of life and death is casted away altogether, and the consumer is made completely immortal to the point in which one is rendered to an irreversibly deathless state, where impossible standards must be met in order for them to be changed back. At this point, no power, force, or manipulation of any kind has any effect. Death at this point is impossible. Anyone who drinks the Hourai Elixir will be forced to live for an eternity with absolutely no exceptions. Unfortunately, the Hourai Elixir only makes one live forever; pain of injuries can still be felt.
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 some, and Kaguya drank 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 who's 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, but at last report, it was in the possession of Fujiwara no Mokou.
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.