I'm not sure about percentage, but I do know that Cuba and DPRK have practically eliminated homelessness. China unfortunately still has homeless people at less than 1 percent of its population, but because of the eradication of absolute poverty and promotion of community centers and social programs, they have better opportunities and living standards than homeless people in other countries.
United Nations Population Fund's summary of DPRK's 2008 census: "Housing is provided by the government free of charge. It is the responsibility of the state to provide housing to everyone. Hence, there is no homeless population." (p. 4)
Unfortunately, I haven't yet double-checked that particular document's authorship (i.e., is it the UNFPA summary as the uploader's description states? Or is it the summary that DPRK's statistics bureau submitted to UNFPA? Or something else?), so take it with a grain of salt and try to verify it if you're going to be using that quote for something.
::: spoiler More info (although not exactly what you asked for, but maybe some will interest you)
DPRK Socio-Economic, Demographic and Health Survey, 2014: This one is co-written by the DPRK's Central Bureau of Statistics and the United Nations Population Fund. There is no specific mention of homelessness in the report but lots of information about housing.
Article: North Korean defector says no homelessness in Pyongyang: "Kim Ryon-hui, the North Korean defector who had said she was tricked into traveling to South Korea by Seoul’s spies in China, said life is better in the North. [...] Kim said South Koreans know very little about life in North Korea, and that upon her arrival in the South, she was surprised by the sight of numerous homeless people in the Seoul subways. Kim said she had never seen homelessness in Pyongyang, because if someone is lost they are taken to their home by a helpful stranger. 'I was surprised that [homeless South Koreans] don't look for their parents or siblings,' she said, stating she had lived in a socialist country for 42 years." (Oddly, this news outlet appears to have been bought at some point by a company connected with the anti-communist Moon organization) (More about Kim Ryon-hui's attempts to return to DPRK and being held in the south against her will)
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Well, there are areas where housing is older and smaller. Like for example, this is in guanzhuo in a poorer neighborhood taken earlier this year.
