A soul can die only in the sense of not having eternal life, which is a state of the soul that is near to God vs. a state of the soul that is far from God. A soul that is far from God is dead in comparison to a holy soul that is near to God so it does not have eternal life. Since Jesus said we would have eternal life (John 3:16, John 3:36, John 17:3, 1 John 5:13, John 5:24, John 11:25-26, John 4:13-14) we know that is in reference to the soul is eternal because the body cannot live forever. It is really that simple.
John 3:16: For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life.
What does not perish? The body perishes, so we know Jesus was referring to the soul.
So whenever the scripture says we lose our soul or our soul dies is that our soul will not attain eternal life. The soul did not attain eternal life because it did not believe in Jesus.
Malachi 4
4 For, behold, the day cometh, that shall burn as an oven; and all the proud, yea, and all that do wickedly, shall be stubble: and the day that cometh shall burn them up, saith the Lord of hosts, that it shall leave them neither root nor branch.
2 But unto you that fear my name shall the Sun of righteousness arise with healing in his wings; and ye shall go forth, and grow up as calves of the stall.
3 And ye shall tread down the wicked; for they shall be ashes under the soles of your feet in the day that I shall do this, saith the Lord of hosts.
4 Remember ye the law of Moses my servant, which I commanded unto him in Horeb for all Israel, with the statutes and judgments.
5 Behold, I will send you Elijah the prophet before the coming of the great and dreadful day of the Lord:
6 And he shall turn the heart of the fathers to the children, and the heart of the children to their fathers, lest I come and smite the earth with a curse.
These verses are all symbolic, not literal. Nothing will literally be burned up. These verses have nothing to do with the afterlife. They are about what will happen on earth in the day of the Lord, which is in reference to when the Christ Spirit returns to earth.
These verses are congruent with what Jesus said about separating the wheat from the chaff.
The proverbial phrase "separate the wheat from the chaff" may not be terribly meaningful to you — unless you happen to be a
grain farmer. The chaff is the husk surrounding a seed, the part of the
grain that is generally thrown away.
chaff - Dictionary Definition : Vocabulary.com
Matthew 13:29-30 King James Version (KJV)
29 But he said, Nay; lest while ye gather up the tares, ye root up also the wheat with them.
30 Let both grow together until the harvest: and in the time of harvest I will say to the reapers, Gather ye together first the tares, and bind them in bundles to burn them: but gather the wheat into my barn.
Harvest time is when Christ returns. The Lord of hosts is the return of Christ. Those that recognize Christ will be gathered together in the barn and those who do not recognize Christ will be burned up or destroyed, metaphorically speaking, because they will be far from God, since they rejected God when God sent His Spirit.