The term rural exodus states is used to refer to those US states which are losing their rural populations in this manner. These states tend to be within the Great Plains and have few scenic amenities, along with harsh summers and severe winters.
In recent years "urban exodus" has also been portrayed as a problem with migrants from towns being seen as unwilling to socialise, having unrealistic expectations of local services (eg.medical and transport facilities) and a cause of accelerating property values to the detriment of potential occupiers born in the locality with lower borrowing and spending power.
See also: demographic history of the United States, rural sociologyUrban Exodus