To answer this question, we should appeal to the BIBLE, GOD'S holy word.
First, who are sinners? They are people who have sinned by coming short of the glory of GOD. Sin is an English word that translates a word from the original language of the Bible, which means "missing the mark." In other words, all humans have missed the mark of PERFECT EXCELLENCE, or "the glory of God." Romans 3:23 states this truth.
The reason we sin is because we are sinners. It is stated in Psalms 51:5 "Behold, I was shapen in iniquity and in sin did my mother conceive me." A rooster does not have to crow once or even twice to become a rooster. He crows because he is a rooster. We do not have to sin to become sinners. We sin because we are sinners.
GOD says, in Romans 6:23, that "the wages (or pay-off) of sin is death." This means eternal separation from GOD, not just physical death. Physical death is a divine appointment for all mankind. (Hebrews 9:27 "And as it is appointed unto men once to die, and after this the judgment.") However, death in hell will mean soul and body in a place of eternal pain and punishment (Matthew 10:28, 25:46). God does not want you to go to hell... it was not prepared for you, but for the devil (Satan) and his angels. (Matthew 25:41 "Then shall He say also unto them on the left hand, 'Depart from me, ye cursed, unto everlasting fire, prepared for the devil and his angles.'")
Jesus Christ, the Son of GOD, died on a tree with the sins of all mankind on Him. Peter, an apostle of the Lord, said "Who His ownself bore our sins in His own body on the tree" (I Peter 2:24). John the apostle said "He is the propitiation (or MERCY SEAT) for our sins; and not for ours only, but also for the sins of the whole world" (I John 2:2).
Please notice that Paul the apostle said to both Jews and Gentiles, "Christ died for the ungodly" (ungodly meaning ALL who are not perfectly GOD-like) Romans 5:6. Can you now confess, in all truth and honesty, that you are a sinner and ungodly and need GOD's salvation?
Jesus said in Luke 19:10 that He (the Son of man) "is come to seek and to save that which was lost." Being lost means we are separated from GOD. One day, a little boy was sobbing mournfully in a department store because he was separated from his mother. He was lost. Some clerks in the store came to his rescue and soon located his mother. She had been very distressed that the boy was lost. So much so was God grieved that He spared not HIS own Son to become a sacrifice for our sins (see Romans 8:32 "He that spared not His own Son, but delivered Him up for us all, how shall He not with Him also freely give us all things?"). GOD demands that sin be judged. Jesus, the Son of GOD was the only person who could qualify to be the sacrifice for the punishment of our sins. (Hebrews 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.") He "died for our sins according to the Scriptures; and that He was buried, and that He rose again the third day, according to the Scriptures" (I Corinthians 15:3-4).
Now to answer the title question in this little message. Yes, GOD will punish lost sinners who die without Jesus Christ as their Savior. Consider Psalm 9:17 "The wicked shall be turned into hell and all the nations that forget GOD." Not because they are sinners, but because they have rejected GOD's own Son to be their Savior. (See II Thessalonians 2:10-12 "And with all deceivableness of unrighteousness in them that perish; because they received not the love of the truth, that they might be saved. And for this cause GOD shall send them strong delusion, that they should believe a lie: That they all might be damned who believed not the truth, but had pleasure in unrighteousness.") Jesus was punished horribly for sinners. He paid the debt and ransom with His precious blood. (See Ephesians 1:7 "In whom we have redemption through His blood, the forgiveness of sins, according to the riches of His grace"; I Peter 1:18-19 "Forasmuch as you know that you were not redeemed with corruptible things, as silver and gold, from your vain conversation received by tradition from your fathers; but with the precious blood of Christ, as of a lamb without spot or blemish"; II Peter 2:1-3 "But there were false prophets, also among the people, even as there shall be false teachers among you, who privily shall bring in damnable heresies, even denying the Lord that bought them, and bring upon themselves swift destruction. And many shall follow their pernicious ways; be reason of whom the way of truth shall be evil spoken of. And through covetousness shall they, with feigned words, make merchandise of you; whose judgment now of a long time lingers not and their damnation slumbers not.")
One question remains: How can I be saved from the wrath to come? (See I Thessalonians 1:10 "And to wait for the Son from heaven, whom He raised from the dead, even Jesus, which delivered us from the wrath to come" and Revelations 6:15-17 "And the kings of the earth, and the great men, the rich men, the chief captains, the mighty men, and every bondsman and every freeman hid themselves in the dens and in the rocks and mountains; and said to the mountains and rocks, "Fall on us and hide us from the face of Him that sitteth on the throne and from the wrath of the Lamb; for the great day of His wrath is come and who shall be able to stand?") Please carefully consider the four (4) things listed below!
REALIZE THAT YOU ARE LOST (Isaiah 59:1-2; Romans 3:10-12, 19, 23; Romans 6:23)
REPENT (meaning change your mind about yourself and your sins) (Mark 1:15; Luke 13:3 & 5; Acts 17:30, 20:21; Romans 2:4; II Corinthians 7:10)
RECEIVE THE WORD OF GOD (James 1:18, 21; I Peter 1:23; John 12:48)
RELY ONLY ON THE LORD JESUS (rely meaning to believe, trust or exercise faith in, commit yourself to the Lord Jesus) (John 3:14-18, 36; John 5:24, 6:47; Romans 10:9-13; Ephesians 2:8-10)
Seek the help and guidance of some Christian if the message of this little tract is not clear to your mind. Praying this will be used of GOD to direct you to the only Savior of sinners, the Lord Jesus Christ, I remain respectfully yours -