Satan told Eve at the tree of Knowledge of Good and Evil that if she ate the fruit of the tree she would not die and the lie about immortality of the soul was born.
God said to Adam, “... in
the day that thou eatest thereof thou shalt surely die ...”. Adam died that day. His body didn’t cease to exist, his soul didn’t cease to exist, and his body & soul didn’t separate. And yet he died that very day. It’s the same death that’s mentioned in
Ephesians 2: ... And you hath he quickened, who were
dead in trespasses and sins ... Even when we were
dead in sins, hath quickened us together with Christ (verses 2 & 6). The Ephesian Christians’ souls existed before they were quickened, and yet they themselves had been dead at the time.
These are all references to
spiritual death; separation from God. Adam & Eve saw that they had separated themselves from God
when their eyes were opened and they saw they were naked and hid themselves.
This is the death that the serpent referenced when he predicted to Eve that she wouldn’t die. Satan didn’t promise the woman that her soul wouldn’t cease to exist and function; he said she wouldn’t die. But she did die, all the while going on to live out her life with an existing and functioning soul. She became
spiritually dead that day.
Be careful not to lift the serpent’s phrase ‘Ye shall not surely die’ out of its context and use it as a buzz-phrase. I don’t know of any
Bible believer who believes in eternal torment for the departed wicked, who doesn’t recognize that spiritual death is what happened to Adam & Eve that day. Death and cessation of existence are two entirely different things.