Carlo Levi was exiled to the south of Italy in 1935 for criticizing Mussolini. Because of what he saw there he wrote the book “Christ stopped at Eboli”. The title came from a local saying that Christ didn’t get any further that the small town Eboli in Campania, about 200km from here. Everybody ignored places like Matera.
Adriano Olivetti of typewriter fame started a plan to build houses closer to the farmlands and relocate people from Matera. In that way the people would not have to travel as far, there would be better services and they would have stables, so they would not have to sleep with the mules all their lives. I think the money for this came from the Marshall Plan in the 1950’s.
Relocating so many people has minuses as well as pluses of course, so apparently it kept sociology researchers busy for years.
There is another town called Crack in Basilicata which has abandoned cave houses. Tourist can visit their, but only with guides. I suppose it was part of the same relocation plan.