I'm not so sure that's true. A not insignificant portion of those people move back out to rural (not suburban) areas to raise families, escape urban burnout, or because of evolving personal tastes. When they do, they often bring significantly more wealth back than they "cost" growing up because of the opportunities they had in the city. It seems that the life and death of a small town depends far more on economic factors like competition from globalization, or environmental fluctuations (droughts, hurricanes, etc). In the US many, if not most, big cities would easily grow from immigration alone.

Obviously cities depend on rural areas since it's far more economical to grow food on cheap plots of land than in steel hydroponic skyscrapers and few cities are built on top of vast fresh water reserves. However, not all rural areas are alike and the majority of the land in the US isnt fertile enough to sustain a competitive agricultural industry like in California, which produces far more of the nation's food and other natural resources than it's share of the population.