Here are a few that more or less support the OP. I typically use the NIV, but in this case I'll go KJ.
The LORD is nigh unto them that are of a broken heart; and saveth such as be of a contrite spirit. Many are the afflictions of the righteous: but the LORD delivereth him out of them all. (Psalms 34:18-19 KJV)
He healeth the broken in heart, and bindeth up their wounds. (Psalms 147:3 KJV)
If iniquity be in thine hand, put it far away, and let not wickedness dwell in thy tabernacles. For then shalt thou lift up thy face without spot; yea, thou shalt be stedfast, and shalt not fear: (Job 11:14-15 KJV)
But if the wicked will turn from all his sins that he hath committed, and keep all my statutes, and do that which is lawful and right, he shall surely live, he shall not die. All his transgressions that he hath committed, they shall not be mentioned unto him: in his righteousness that he hath done he shall live. (Ezekiel 18:21-22 KJV)
But go ye and learn what that meaneth, I will have mercy, and not sacrifice: for I am not come to call the righteous, but sinners to repentance. (Matthew 9:13 KJV)
If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness. (1 John 1:9 KJV)
Repent ye therefore, and be converted, that your sins may be blotted out, when the times of refreshing shall come from the presence of the Lord; (Acts 3:19 KJV)