How can someone who has committed grave sins—such as adultery and injustice—live a life of purity after repentance, especially when a person who has committed adultery may remain "fallen in the eyes of people," even if they have repented?

Allah accepts the repentance of the sinner and transforms his evil deeds into good ones. One who repents from a sin is like one who has committed no sin, and he is beloved by Allah. The repentant person must be sincere in his repentance by fulfilling its conditions, abandoning evil companions, striving in acts of obedience, adhering to good morals, holding himself accountable, demonstrating chastity and truthfulness, and supplicating that Allah may draw the hearts of His servants to Him. His believing brethren should accept the repentant person, support him, and neither punish nor blame him. If the situation does not improve for the repentant person in his environment, then he is advised to change his location to a righteous environment, as in the story of the man who killed ninety-nine souls.