While we don't have exact precise numbers for the total homeless population of the USSR, we know several facts that point to it being extremely low, close to no rate of homelessness.

Firstly, the USSR passed laws aiming for the abolition of homelessness in different regions throughout the 1930s. This implemented itself differently depending on the area, but for example: the Systemization process in Romania (active during the 1970s) led to the demolishing and reconstruction of many structures, many being buildings and blocks for housing that were often offered at discount prices for working people and near or totally free for older ages (usually being old people who had no family to live with, otherwise often they simply lived with their family that could afford the cheaper housing). This type of housing usually was done as blocks with a small number of bedrooms, a bathroom, a kitchen and a living room, as well as a pass to freely edit the structure of the apartment to the individuals needs (turning the living room into a bedroom, etc). This type of program was implemented at different types in different ways across the USSR, aimed at reducing homelessness to 0. Within Russia the program was known as Communal Housing and started much earlier.

Secondly, the lack of private landlords and the lack of ownership of multiple housing units by private citizens. Most housing was either subsidized to a reduced cost or near nothing in certain cases, but there were small forms of rental housing. These were known as Propinskas within the USSR, and generally were used by 2 groups of people. Long tern migeants, either seeking to move permanently or stay for an extended period but lacked citizenship would be living as tenants to the state within Propinska housing. The second group were workers who had to work far away from home, known as industry Propinskas. These industry's rented housing was often rented at very low prices to workers who had to travel for their jobs, and were meant to be temporary. There is little evidence of permanent living in rent hinting that most people had access to housing, and that rent was not a norm , as people were able to afford permanent housing outright or had sufficient family housing

Thirdly, the large spike in homelessness after the dissolving of the USSR. A large amount of metrics crashed after its dissolving, including GDP per capita, poverty rate, calories eaten per day, infant mortality rate, etc. We know a fair amount about these metrics, and that they were fairly low throughout the USSR. This implies homeless was also a low number, which spiked along with other metrics in 1991.