The soul cannot die because it is immortal. What the Bible means is that the soul that sins will not have eternal life.
When Jesus referred to
eternal life, but He was not referring to physical life of the body. He was referring a quality of life,
spiritual life, loving God and being close to God, and we can have eternal life both in this world and in the next world (the spiritual world).
All the verses below refer to eternal life of the soul, not life of the physical body.
John 11:25-26 Jesus said to her, “I am the resurrection and the life. He who believes in Me, though he may die, he shall live. And whoever lives and believes in Me shall never die. Do you believe this?”
John 3:16 For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but haveeternal life.
1 John 5:13 I write these things to you who believe in the name of the Son of God that you may know that you have eternal life.
John 5:24 Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting life, and shall not come into condemnation; but is passed from death unto life.
All souls continue to exist in the spiritual world after the body dies but not all souls have eternal life (everlasting life).
Eternal life refers to a “quality” of life, nearness to God which, according to Jesus, comes from believing in Him.
“The immortality of the spirit is mentioned in the Holy Books; it is the fundamental basis of the divine religions. Now punishments and rewards are said to be of two kinds: first, the rewards and punishments of this life; second, those of the other world. But the paradise and hell of existence are found in all the worlds of God, whether in this world or in the spiritual heavenly worlds. Gaining these rewards is the gaining of eternal life. That is why Christ said, “Act in such a way that you may find eternal life, and that you may be born of water and the spirit, so that you may enter into the Kingdom.” 2 ” Some Answered Questions, p. 223
“Likewise, the rewards of the other world are the eternal life which is clearly mentioned in all the Holy Books, the divine perfections, the eternal bounties and everlasting felicity….The rewards of the other world are peace, the spiritual graces, the various spiritual gifts in the Kingdom of God, the gaining of the desires of the heart and the soul, and the meeting of God in the world of eternity.”
Some Answered Questions, pp. 224-225
Those people who are distant from God do not have eternal life, although their soul continues to exist in the spiritual world after their physical body dies.
“In the same way, the souls who are veiled from God, although they exist in this world and in the world after death, are, in comparison with the holy existence of the children of the Kingdom of God, nonexisting and separated from God.” Some Answered Questions, p. 243