Meanwhile in USSR times:
You could not bequeath your flat in USSR, because you had not bought it , but "получал" instead (from State). Relatives (children usually) usually could continue to live in the same flat, if they were living there before death of "main inhabitant" (были прописаны).
And conversely, people were buying cars, so could pass them to relatives (I think so, don't remember exactly).
On the other hand you didn't pay a kopeck for the flat received from the state, so it was not ethically right to have such pretensions. Those flats that were built in cooperatives could be inherited as well as private houses with the plots of land. Even land share in collective farms (земельные паи в колхозах) could be inherited. I know it for sure, because my grandparents were колхозники and my father inherited their land share and house with a plot of land.