I believe the Bible teaches that when a sinner comes to faith in Christ, God gives that person a new birth and places him spiritually "in Christ" so that spiritually speaking, we become united with Christ in his suffering and death. That is, God punished us "in Christ," which is how His justice is satisfied.
2 Cor. 5:17 Therefore, if anyone is in Christ, he is a new creation; the old has gone, the new has come!
Rom. 8:1 Therefore, there is now no condemnation for those who are in Christ Jesus..."
Rom. 6:4-8: We were therefore buried with him through baptism into death in order that, just as Christ was raised from the dead through the glory of the Father, we too may live a new life.
5 If we have been united with him like this in his death, we will certainly also be united with him in his resurrection. 6 For we know that our old self was crucified with him so that the body of sin might be done away with, that we should no longer be slaves to sin-- 7 because anyone who has died has been freed from sin. 8 Now if we died with Christ, we believe that we will also live with him."
Eph. 4:32 Be kind and compassionate to one another, forgiving each other, just as in Christ God forgave you.
Eph. 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, 14 who is a deposit guaranteeing our inheritance until the redemption of those who are God's possession-- to the praise of his glory.
Eph. 2:13-16 But now in Christ Jesus you who once were far away have been brought near through the blood of Christ. 14 For he himself is our peace, who has made the two one and has destroyed the barrier, the dividing wall of hostility, 15 by abolishing in his flesh the law with its commandments and regulations. His purpose was to create in himself one new man out of the two, thus making peace, 16 and in this one body to reconcile both of them to God through the cross, by which he put to death their hostility.
1 Peter 2:24 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.
Col. 2:9-14 For in Christ all the fullness of the Deity lives in bodily form, 10 and you have been given fullness in Christ, who is the head over every power and authority. 11 In him you were also circumcised, in the putting off of the sinful nature, not with a circumcision done by the hands of men but with the circumcision done by Christ, 12 having been buried with him in baptism and raised with him through your faith in the power of God, who raised him from the dead. 13 When you were dead in your sins and in the uncircumcision of your sinful nature, God made you alive with Christ. He forgave us all our sins, 14 having canceled the written code, with its regulations, that was against us and that stood opposed to us; he took it away, nailing it to the cross.
1 Cor. 1:30 It is because of him that you are in Christ Jesus, who has become for us wisdom from God-- that is, our righteousness, holiness and redemption.
1 Cor 15:22 For as in Adam all die, so in Christ all will be made alive.
2 Tim. 2:10-13 Therefore I endure everything for the sake of the elect, that they too may obtain the salvation that is in Christ Jesus, with eternal glory. 11 Here is a trustworthy saying: If we died with him, we will also live with him; 12 if we endure, we will also reign with him. If we disown him, he will also disown us; 13 if we are faithless, he will remain faithful, for he cannot disown himself.