I remember a movie where a boy stole food because he was hungry and the policeman who chased him that day never forgot him and chased him down years later when the boy was an adult. The movies was probably made in the 80’s (color) and the film was set in the early 1900’s I believe.
The plot you describe is basically Victor Hugo’s “Les Miserables.” It’s been adapted for film many times. Here is a partial list: http://en.wikipedia.org/wiki/Adaptations_of_Les_Mis%C3%A9rables. The 1978 British television movie with Anthony Perkins might be a candidate. Good luck.