Right after the saints are caught up to meet Jesus in the air, seven angels will come forth and they will pour out the seven bowls of the wrath of God. The saints(believers) will no longer be on the earth. The apostle Paul wrote in his letter to the Romans, in the 5th Chapter, verses 8 and 9;
(8)"But God demonstrates His own love for us, in while we were yet sinners,
Christ died for us. (9) Much more then, having now been justified by His blood,
we shall be saved from the wrath of God through Him."
Paul again writes in his first letter to the Thessalonians, in Chapter 1, verse 10 and Chapter 5, verse 9:
(1:10)"and to wait for His Son from the heavens, whom He raised from the dead,
that is Jesus, who delivers us from the wrath to come."
(5:9)" For God has not destined us for wrath, but for obtaining salvation through
our Lord Jesus Christ."
There are a few reasons that we know why the wrath of God will come. We know that one of the reasons is revealed in the Book of Revelation, Chapter 11, verse 18;
"And the nations were enraged, and Thy wrath came, and the time came for the
dead to be judged, and the time to give their reward to Thy bond-servants the
prophets and to the saints and to those who fear Thy name, the small and the
great, and to destroy those who are detroying the earth."
The wrath of God is coming to destroy those who are destroying the earth. For three and a half years after Satan is cast out of heaven and down to the earth, Satan will go on a campaign of destruction such has never been. That is why Paul refered to Satan as the 'son of destruction', in his second letter to the Thessalonians, Chapter 2, verse 3. Jesus stated in the 24th Chapter of Matthew in Chapter24, verse 22;
"And unless those days had been cut short, no life would have been saved;
but for the sake of the elect those days shall be cut short."
The people who are still on the earth when the wrath comes, are those who would not receive the truth of salvation as to be saved. Paul wrote this in his 2nd letter to the Thessalonians, Chapter 2, verse 12;
"in order that they all may be judged who did not believe the the truth, but took
pleasure in wickedness."
Again Paul writes in his letter to the Romans, in Chapter 1, verse 18;
"For the wrath of God is revealed from heaven against all ungodliness and
unrighteousness of men, who suppress the truth in unrighteousness."
In the 2nd letter by Paul to the Thessalonians, in the 2nd Chapter, verse10, Paul writes;
"and with all deception of wickedness for those who perish, because they
did not receive the love of the truth so as to be saved."
People will be left on earth to have to go through the wrath of God, only because they did not want to receive Jesus' free gift of eternal life. Instead they chose to be stubborn and refuse Jesus' offer and therefore suffer the consciquence of doing so. Again, I can not quote this passage enough because it shows the heart and desire of God. It is what Peter wrote in his 2nd letter, Chapter 3, verse 9;
"The Lord is not slow about His promise, as some may count slowness, but is
patient toward you, not wishing for any to pershish but for all to come to
repentance."
May Jesus' peace and grace be with you.