Yes, but the culture adopted can extend being poor, or it can help the economy. The South and Appalachia still have cultures that don't value industriousness or education generally. They aren't known for it. So when the coal or cotton goes away, the culture extends being poor.

Seems a bit unfair to go blaming the victim there, and attributing poverty to just not "valuing industriousness" enough.

The economic fortunes of the South and Appalachia are also deeply affected by history and geography. Centuries ago they built their economies on slavery and agriculture - and bear the scars of those decisions today.

And they were crushed by the Second Industrial Revolution, especially the development of the railroad...because of the Appalachian Mountains. While the North and Midwest were being knit together in an economic engine by the development of railway transportation, linking the center of the country to the coastal ports with low-cost/high-volume transport, the South and Appalachia were basically cut off from all of that by a dominant mountain range:

appalachian-railroads.org - Railroads across the appalachians.

The entire region basically missed out on nearly a century railroad-oriented economic development, from the Civil War until the development of the interstate highway system and air travel. The major East-West economic engine ran north of the mountains, from the major cities of the Great Lakes eastward to the major Northeastern ports in Boston and New York.