According to Jesus and the Bible, yes the soul can die as is seen in the next three pasted verses.
Mt 10:28 And fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell.
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.
Eze 18:20 The soul that sinneth, it shall die. The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be upon him, and the wickedness of the wicked shall be upon him.
It is reasonable to ask then, what about the “eternal fire” aspect?
The most quoted verse in the defense of the concept of eternal torment is in my opinion Matthew 25:46.
Mt 25:46 And these shall go away into everlasting punishment: but the righteous into life eternal.
The answer to the seeming contradiction of the verses quoted is found by comparing the following two verses.
Mt 25:41 Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:
Heb 2:9 But we see Jesus, who was made a little lower than the angels for the suffering of death, crowned with glory and honor; that he by the grace of God should taste death for every man.
Angels do not die as Heb 2:9 tells us, and Hell or everlasting fire was made as punishment for them. Since they don’t die their punishment is eternal.
Since the reward for obedience is righteousness joy and peace in the Holy Spirit (Rm 14:17) the penalty for disobedience then is the lack of the reward.
Romans 14:17 KJV — For the kingdom of God is not meat and drink; but righteousness, and peace, and joy in the Holy Ghost.
They dwell there and they do not die.
Hence the term everlasting fire.
The Bible answers both questions –
Can the soul of man die – yes.
Is Hell fire eternal – yes.
During this lifetime on earth, a person can be delivered into the place where the Devil and His angels are confined.
This place is called “everlasting fire” or “Hell”.
A person can also be released from this place as is seen in Matthew 5:26.
Mt 5:26 Verily I say unto thee, Thou shalt by no means come out thence, till thou hast paid the uttermost farthing.
Being delivered into Hellfire because of disobedience to God is a punishment during this lifetime, not unlike a parent disciplining His Child. If a person goes there after death as a result of a life of unbelief their soul is destroyed according to Jesus Christ, Mt 10:28.
Matthew 10:28 KJV — And fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell.