Rural Italy is beautiful and the food (in the grocery stores and markets) is both great and ridiculously cheap. But there are a few downsides. 100-plus-year-old houses often require significant refurbishment including earthquake mitigation (depending on the area) and they can be expensive to heat unless you spend $$$ on new windows and good seals and insulation. But the biggest problem for a foreigner moving to Italy might be the bureaucracy: Huge stacks of paper forms to be filled out and handed in to a guy who just happens not to be in his office today. Repeatedly. If you have a lot of patience for this sort of thing, Italy is lovely.
Also, if you do a job that is defined in law (doctor, architect, journalist, etc), the bureaucracy might actually stop you from working until you’ve jumped several hoops - exams, payments, years of practice, and so on.
Hmm... I was too lazy to do the Google search, sorry about that. I figured the average HN type would prefer to do a DYOR Google search anyway. I happened to have seen it on a Dutch program (a Dutch couple moved to Italy).
I know of a few places with schemes to incentive people to move to dying towns, in the regions bordering with Northern Appennini mountains and in the deep South. The catch is that these towns are dying for a reason: they are far from everything, there are no local jobs (or rather, no jobs most people would do - being a farmer in 2018 is unappealing), and the housing stock is often crumbling and centuries-old. The kids go to school in cities and never go back, so you’re left with a bunch of oldies. Do not expect any help from the State, but do expect hindrance, especially in building matters - Italian laws on paper are the best in the world, but in practice, compliance is hell.
