They may have existed somewhere, but I'm not aware of any in my home town.
As with many things in the USSR, it may well have been regional and time-dependent. My memories are from mid-80s, although I know that my family had one before then. I didn't know anyone whose family didn't have one, and we weren't a nomenklatura family or anything like that - just a regular Soviet family with boring everyday jobs (teachers and engineers) - and neither were our neighbors and acquaintances.
As with many things in the USSR, it may well have been regional and time-dependent. My memories are from mid-80s, although I know that my family had one before then. I didn't know anyone whose family didn't have one, and we weren't a nomenklatura family or anything like that - just a regular Soviet family with boring everyday jobs (teachers and engineers) - and neither were our neighbors and acquaintances.