Which movie ends like this:

American movie, I only remember the end scene, which was something like this:
A father- if I remember well- drove his son to the jail for his sentence, and on the way he offered him to drop him over the border instead to start a new life with a new identity. He advised him not to contact his girlfriend anymore, so maybe, only maybe one day the girlfriend will show up, and they will start a family
During the conversation they were showing black and white scenes about this imaginary future, where the convicted son grew old, and he was surrounded with grandchildren.
Anybody could advise, which movie was this?
Thank you