Part of what I like about the movie (aside from the songs and the stories) is the dramatic irony -- we know what is likely to happen to the characters in the years after the movie. Havala moves to Krakow, site of a future notorious concentration camp. Not good for Havala. The middle daughter marries her communist boyfriend, though the communists probably killed their Jewish supporters (just speculating). At the least, they were forbidden to practice their religion. Tevia moves to America, Chicago, where he probably sets up a dairy company and becomes a rich man. God answers his prayers.
At least that's what I imagine as "the rest of the story" for Tevia.
"Tevia moves to America, Chicago, where he probably sets up a dairy company and becomes a rich man. God answers his prayers."
YES! And he gets to spend lots of time studying Torah. :-)