Immortals

Immortals (不老不死 , furoufushi) are organisms who cannot die under normal circumstances like age. Immortality is divided into two separate groups; one that is based on folklore and the other being based on science. The scientific image of immortality is different than what immortality is often portrayed in religion or popular culture.
In folklore, those who obtained immortality cannot die regardless what happens to them. More often than not, immortals are restrained, sealed, or imprisoned. A human who is immortal is often considered to have committed a spiritual crime. Spirits and Gods are seen as immortal in many religions as well. Undead beings like the Jiang Shi are immortal to some extent, seeing as they can be resurrected after death, however they are technically considered dead and not immortal.
In science, bioligical immortality (生物学における不老不死 , seibutsugaku-ni-okeru-furoufushi) is the only form of immortality 
theoretically achievable and has been seen in nature. This form prevents an organism's death as long as it is not physically harmed, unlike in immortality seen in folklore. Bioligical immortality has only been seen in few organisms, such as the Turritopsis nutricula jellyfish. In some religions, gods are biologically immortal as they do not die from age but by injury from other gods or other creatures.
In Touhou there are quite a few biological immortals, such as the lunarians or hermits. Spirits like yuurei andonryou are also biologically immortal seeing as they can be killed by characters like Youmu Konpaku or Kasen Ibara who have the ability to dispose of such beings. However, because they are non-living/dead, they cannot be classified as immortals. Only a few characters in the series are pure immortals. Those who have 
taken theHourai Elixir are known as the "people of hourai" (蓬莱人, houraibito or houraijin). Currently, this is the only known method to obtain pure immortality.
* Examples of true immortals: Kaguya Houraisan, Fujiwara no Mokou , Eirin Yagokoro