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Anecdotal data from Poland : mostly, yes, they are owned by people living in them, or by people renting them (people having small amount of apartments that they are renting). Mind you - in post-communist countries, in cities houses are not as popular as apartments, as we do not have USA-style suburbs.

There is issue on the housing (apartment?) market, but it has nothing to do with communism, mostly with capitalism - big funds are buying apartments en masse (mostly new ones) and a lot of people started buying previously cheap apartments and renting them, causing prices to skyrocket in the last years.