Breath

A married woman, Yeon, struggling with her husband's infidelity, finds solace in the unlikeliest of places - the prison cell of a condemned criminal, Jin, who has attempted suicide multiple times. Despite his dark past, Yeon sees a deep sadness in Jin and decides to visit him regularly, eventually developing a strong bond. As their relationship grows, Yeon's husband becomes increasingly jealous and tries to put an end to her visits, but she continues to see Jin, finding a sense of purpose and love in his company.

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Some movies that have similar genres and were produced around the same time as Breath include Before the Devil Knows You're Dead, The Departed, The Dark Knight, The Town, Freedom Writers, Unthinkable.