The Soviet system wasn't oriented toward the mass production of automobiles for internal consumption the same way as say the US, but there were vehicles produced for those from among 'the masses' that wanted or really needed a car for personal use. Cars were affordable if you were willing and able to save up from your earnings of the course of many years to make the purchase. There were no incentive programs, as far as I'm aware, again because the system was designed to attempt to meet existing demand, not to create new demand via credit, leasing, etc.
The Niva was among these cars for the masses, and probably among the best in terms of durability and practicality. You can still see plenty of actual Soviet Nivas (distinguished by their rear headlights) driving around Russian cities, though not so much in Moscow. You're right Yami that they were designed for offroad conditions, and a few owners I've spoken to have told me that they're not as comfortable to drive in the city. They all had positive recollections of the car, especially the guy that lived in a mountain village with poor roads. One guy did say his car had its problems, though most of them were covered under warranty. He thinks it's because it was built on a Monday (just as with the Big Three in North America, Soviet cars built on Mondays and Fridays seemed to share the problems of laziness/sloppiness component installation).
What amazes me about the Niva is that even today it remains probably the best mass-produced offroad vehicle out there, even if it's not luxurious, like many of its contemporaries. There's many a video on youtube showing Hummers and Range Rovers getting stuck in conditions that Niva easily passes through. The simplicity and durability of the design, like much of Soviet production, is what seems to bring admiration for the Niva.