“What happens when a forgiven believer in Jesus sins?”
Since the questions has everything do with our relationship with God, sin, and grace, your answer will dramatically affect how the questioner views the gospel of Jesus. Therefore, it’s a question to ponder deeply and prepare to answer succinctly.
John Bunyan’s Answer
John Bunyan helps answer the question, “What happens to a believer’s relationship with God when they sin?”
Sin, after the Spirit of adoption (has) come, cannot dissolve the relation of father and son, of father and child . . . Now mark, you are no more a servant, that is, no more under the law of death and damnation, but a son, and if a son, then an heir of God through Christ (Galatians 4:4-7).
Suppose a child grievously transgresses against and offends his father, is their relationship therefore dissolved? Again, suppose the father should (discipline) the son for such offense, is the relationship between them therefore dissolved? Even more, suppose the child should now, through ignorance, cry, and say, “This man is now no more my father!” is he therefore now not his father? Does not everyone see the folly of such thinking?
Know, then, that your sin, after you have received the Spirit of adoption to cry unto God, “Father! Father!” is counted the sin of a child, not of a slave, and that all that happens to you for that sin, is but the discipline of a father. “What son is he whom the father disciplines not?” (Hebrews 12:1).
(Taken from The Fear of God, p. 47-48)
The London Baptists’ Answer
God has granted that all those who are justified would receive the grace of adoption, in and for the sake of his only Son Jesus Christ.1 By this they are counted among the children of God and enjoy the freedom and privileges of that relationship.2 They inherit his name,3 receive the spirit of adoption,4 have access to the throne of grace with boldness, and are enabled to cry “Abba, Father!”5 They are given compassion,6 protected,7 provided for,8 and (disciplined) by him as a father.9 Yet they are never cast off10 but are sealed for the day of redemption11 and inherit the promises as heirs of everlasting salvation.12
1Ephesians 1:5; Galatians 4:4, 5. 2John 1:12; Romans 8:17. 32 Corinthians 6:18; Revelation 3:12. 4Romans 8:15. 5Galatians 4:6; Ephesians 2:18. 6Psalms 103:13. 7Proverbs 14:26. 81 Peter 5:7. 9Hebrews 12:6. 10Isaiah 54:8, 9; Lamentations 3:31. 11Ephesians 4:30. 12Hebrews 1:14; 6:12.
And here is another part (article 11) of the same confession.
God continues to forgive the sins of those who are justified.14 Even though they can never fall from a state of justification,15 they may fall under God’s fatherly displeasure because of their sins.16 In that condition they will not usually have the light of his face restored to them until they humble themselves, confess their sins, plead for pardon, and renew their faith and repentance.17
14Matthew 6:12; 1 John 1:7, 9. 15John 10:28. 16Psalms 89:31–33. 17Psalms 32:5; Psalms 51; Matthew 26:75.
There is definitely more that could be said, but these answers, and the Scriptures therein, will serve you well as you seek to help others live within the finished work of Christ and enjoy their blood bought adoption as sons & daughters of God.