Obviously, when it comes to details, different revolutions play out differently.
In the Soviet Union, after the 1917 revolution a decree abolished (1) the right to own vacant land in a city (i.e. land with no building on it); and (b) the right to own land with a building in a city, if the value of the land + building exceeded an amount set by the city government. In both cases, the land/buildings became the property of the city government. Those in occupation of the land/buildings could continue to occupy, but would have to pay market rent (which they might already be doing, of course, if they had been tenants of the expropriated owners). An expropriated owner, if unable to work and having no other means of subsistence, could get compensation up to 10,000 rubles. (I have no idea what kind of purchasing power 10,000 rubles might have represented in 1918.)
The effect of this was that if you owned a modest building in a city (whether it was your home or, e.g., your shop or workshop), you got to keep it, with the city government deciding the value threshold that would determine who got to keep their buildings and who had them expropriated. How scrupulously this decree was respected by city governments in the chaotic and volatile early years of the Soviet Union is another matter, of course, but basically it established in principle that private ownership of modest buildings was not forbidden.
The Soviet Constitution, adopted in 1936, affirmed the right of private ownership of (among other things) your own dwelling-house, and the right to bequeath it to your heirs.
In the mid-1950s it was estimated that about a third of housing stock in the Soviet Union was privately-owned. You could also get land from the state to build a new house on; you didn’t own the land, but you held it in “perpetual tenure”, subject only to the payment of a modest ground rent. If you sold your house, the perpetual tenure of the land on which the house stood automatically went with it.
So, basically, it was not the default position that your home was forfeited to the state after the revolution, or that you had to pay rent to continue living in it. But, the larger and more valuable your home was, the more likely it was that it would be forfeited to the state.