I was curious about this claim. A 2004 study of ~500 homeless adults in Pennsylvania found that roughly 70% reported that they did not use more drugs after becoming homeless, though about 80% reported regularly using drugs [1]. But there are other studies that claim the opposite, for example this 1990 study of ~1400 homeless adults in California that finds "[p]revalences of alcohol abuse, illegal drug use, and psychiatric hospitalization when adults first became homeless were 15% to 33% lower than prevalences following homelessness". But it's hard to dig into the second result, because the paper is paywalled, like most of the papers about this topic.

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1448345/

[2] https://ajph.aphapublications.org/doi/abs/10.2105/AJPH.82.10...