Why did Elimelech's family leave Bethlehem and move to Moab?

Answer: There was a famine

In the days when the judges ruled, there was a famine in the land, so the family went to reside in Moab.

“In the days when the judges ruled, there was a famine in the land. And a certain man from Bethlehem in Judah, with his wife and two sons, went to reside in the land of Moab.”— Ruth 1:1 (BSB)