You'd be surprised at how humans "make a plan" when it comes to those things, as long as family/community is not broken. Either way, there probably was some homelessness, but we'd have to look at actual records/stats on it.
But the USSR was just one system of social housing. Have a look at what's happening right now in South Africa with what they call RDP housing:
Since it was a subject of official denial, records and stats would likely be hard to find.