Mike asks all of the right questions. It is an interesting notion, but we all know there is no such thing as a free lunch (as the saying goes). Having said that, something like this has always been my dream. I've traveled around the world a fair amount over the years and everywhere I went I asked myself, could I live here when I retire?
I saw one example of these affordable Italian homes on TV. A American couple purchased and renovated one in southern Italy; if I recall they paid something like $15-20K USD for the home and more than that again to redo it. It did not have running water, any electricity, no heat/air, etc. The floors were a treated hard dirt surface, the structure was bare stones, opening for windows but no actual glass windows, one wooden door that fit loosely, no lights, etc. A fireplace type structure was for heat as well as cooking (no real kitchen let alone stove, appliances). Basically a primitive two room structure. I think most Americans could not live in such a dwelling, we are way too spoiled. But these are buildings that were built a very long time ago in outlaying areas where people did things like farming.
I'm not saying this is what all of them are like, just the one I happened to see featured on one of those home refurbishing TV shows. It would be very interesting to learn more. Some parts of Italy have rather harsh (hot dry) weather, but others are quite nice. While common sense tells me you will not find a $1 house in the nicer areas, it is something to look further into.
Another interesting area I've heard about is in southern Spain. Apparently some developers built several 'cities' in hopes of it becoming a booming new region. But then financial collapse came and none of the homes were ever sold and the cities never finished. They were modern structures in a beautiful area. It's my understanding they are all still sitting abandoned to this day. No idea if any of it could be purchased but it would be intriguing.
I believe (but do not know) that economic reasons are what's behind the 'cheap' houses available in places like Italy and others. They have long histories of severe financial problems, making the areas unlivable for the previous residents (no sources of income, etc). Depending on your specific situation this may be a good or bad thing.
I was attracted to some small tropical islands in the Caribbean several years ago. Looked like a really nice place to retire. But after further investigation I learned two things; 1) the local realtors (and governments) were wise to American buyers and multiplied the prices several fold for foreigners (making it very unaffordable), and 2) there is not much in the way of car culture to be found in such places, eventually making it boring for me.
Hope to hear more about the Italian opportunities, I still haven't decided where I will retire but it likely won't be in the US.