Answer: The second time Jesus appears will NOT be to bear, or take away, the sins of many people. No, the second time Jesus appears will be to bring salvation to those people who believed in Him and obeyed Him, and who are waiting for Him, (verse 28).
MORE INFORMATION AND/OR OTHER SCRIPTURE REFERENCES:
"...and He will appear a second time..."
Matthew 16:27: [Jesus said,] "For the Son of Man is going to come in His Father's glory with His angels, and then He will reward each person according to what he has done."
John 14:1-4: [Jesus said,] "Do not let your hearts be troubled. Trust in God; trust also in Me. In My Father's house are many rooms; if it were not so, I would have told you. I am going there to prepare a place for you. And if I go and prepare a place for you, I will come back and take you to be with Me that you also may be where I am. You know the way to the place where I am going."
Acts 1:9-11: "After He [Jesus] said this, He was taken up before their very eyes, and a cloud hid Him from their sight. They were looking intently up into the sky as He was going, when suddenly two men dressed in white stood beside them. ‘Men of Galilee,' they said, ‘why do you stand here looking into the sky? This same Jesus, Who has been taken from you into heaven, will come back in the same way you have seen Him go into heaven.'"
"...not to bear sin..."
1 Peter 2:24-25: "He Himself bore our sins in His body on the tree, so that we might die to sins and live for righteousness; by His wounds you have been healed. For you were like sheep going astray, but now you have returned to the Shepherd and Overseer of your souls."
Hebrews 7:27: "Unlike the other high priests [under the Old Law of Moses], He [Jesus] does not need to offer sacrifices day after day, first for His Own sins, and then for the sins of the people. He sacrificed for their sins once for all when He offered Himself."
"...but to bring salvation..."
Hebrews 5:9: "and, once made perfect, He became the source of eternal salvation for all who obey Him."
Luke 3:6: "And all mankind will see God's salvation."
Acts 4:12: "Salvation is found in no one else, for there is no other name under heaven given to men by which we must be saved."
Ephesians 1:13-14: "And you also were included in Christ when you heard the Word of Truth, the Gospel of your salvation. Having believed, you were marked in Him with a seal, the promised Holy Spirit, Who is a deposit guaranteeing our inheritance until the redemption of those who are God's possession--to the praise of His glory."
1 Thessalonians 5:9: "For God did not appoint us to suffer wrath but to receive salvation through our Lord Jesus Christ."
1 Peter 1:3-9: "Praise be to the God and Father of our Lord Jesus Christ! In His great mercy He has given us new birth into a living hope through the resurrection of Jesus Christ from the dead, and into an inheritance that can never perish, spoil or fade--kept in heaven for you, who through faith are shielded by God's power until the coming of the salvation that is ready to be revealed in the last time. In this you greatly rejoice, though now for a little while you may have had to suffer grief in all kinds of trials. These have come so that your faith--of greater worth than gold, which perishes even though refined by fire--may be proved genuine and may result in praise, glory and honor when Jesus Christ is revealed. Though you have not seen Him, you love Him; and even though you do not see Him now, you believe in Him and are filled with an inexpressible and glorious joy, for you are receiving the goal of your faith, the salvation of your souls."
"...to those who are waiting for Him."
1 Corinthians 1:7-9: "Therefore you do not lack any spiritual gift as you eagerly wait for our Lord Jesus Christ to be revealed. He will keep you strong to the end, so that you will be blameless on the day of our Lord Jesus Christ. God, Who has called you into fellowship with His Son Jesus Christ our Lord, is faithful."
1 Thessalonians 1:4-10: "For we know, brothers loved by God, that He has chosen you, because our Gospel came to you not simply with words, but also with power, with the Holy Spirit and with deep conviction. You know how we lived among you for your sake. You became imitators of us and of the Lord; in spite of severe suffering, you welcomed the message with the joy given by the Holy Spirit. And so you became a model to all the believers in Macedonia and Achaia. The Lord's message rang out from you not only in Macedonia and Achaia--your faith in God has become known everywhere. Therefore we do not need to say anything about it, for they themselves report what kind of reception you gave us. They tell how you turned to God from idols to serve the living and true God, and to wait for His Son from heaven, Whom He raised from the dead--Jesus, Who rescues us from the coming wrath."
1 Thessalonians 2:19: "For what is our hope, our joy, or the crown in which we will glory in the presence of our Lord Jesus when He comes? Is it not you?"
Titus 2:11-14: "For the grace of God that brings salvation has appeared to all men. It teaches us to say ‘No' to ungodliness and worldly passions, and to live self-controlled, upright and godly lives in this present age, while we wait for the blessed hope--the glorious appearing of our great God and Savior, Jesus Christ, Who gave Himself for us to redeem us from all wickedness and to purify for Himself a people that are His very Own, eager to do what is good."
James 5:7-8: "Be patient, then, brothers, until the Lord's coming. See how the farmer waits for the land to yield its valuable crop and how patient he is for the autumn and spring rains. You too, be patient and stand firm, because the Lord's coming is near."
1 Peter 1:13: "Therefore, prepare your minds for action; be self-controlled; set your hope fully on the grace to be given you when Jesus Christ is revealed."
2 Peter 3:11-15: "Since everything will be destroyed in this way, what kind of people ought you to be? You ought to live holy and godly lives as you look forward to the day of God and speed its coming. That day will bring about the destruction of the heavens by fire, and the elements will melt in the heat. But in keeping with His promise we are looking forward to a new heaven and a new earth, the home of righteousness. So then, dear friends, since you are looking forward to this, make every effort to be found spotless, blameless and at peace with Him. Bear in mind that our Lord's patience means salvation, just as our dear brother Paul also wrote you with the wisdom that God gave him."
Jude 1:21: "Keep yourselves in God's love as you wait for the mercy of our Lord Jesus Christ to bring you to eternal life."