Here, again, the word "soul" is translated into English from the Hebrew and Greek terms described in the article -- but the meaning is that by breathing His breath into Adam, man came to life. Thus physical death occurs when that "life force" leaves the body and either goes back to God or doesn't.
Eastern Christianity teaches that God does not reject the soul, but rather that the soul rejects God. If the "soul" is God's breath, then it certainly cannot die, for everything of God is eternal, and "life force" is no different. Thus, souls that reject God at the moment of death, eternally condemn themselves to that separation forever. Normally souls die:
Jam 5:20 Let him know, that he which converteth the sinner from the error of his way shall save a soul from death, and shall hide a multitude of sins.
Eze 18:4 Behold, all souls are mine; as the soul of the father, so also the soul of the son is mine: the soul that sinneth, it shall die.
Psa 116:8 For thou hast delivered my soul from death, mine eyes from tears, and my feet from falling.
Soul is life and life comes from God and is of God and as such life is eternal. The death of a soul is spiritual, not physicial.