Ugh, this is a horrible article. 45% of people found housing, but there was zero difference between the treatment group (given $1,000/month), a group given a large lump sum, and a control group given $50 a month!
https://www.denverbasicincomeproject.org/research
A lot of people rotate in and out of homelessness, so we should expect some percentage to find housing after a year, even if nothing is done. Indeed, this seems like pretty strong evidence that giving more money does not help people find housing (at least in the range from $50/month to $1,000/month).
They cite a decrease in public service costs, but again, there is no difference between treatment and control! See page 6 in this PDF: https://static1.squarespace.com/static/64f507a995b636019ef88...
They calculate "saved costs" by estimating the difference in costs between the start of the program (a year ago) and a year into the program (now). However, since they are tracking a particular group of people, some of them will find homes and jobs on their own, so we should expect costs for that cohort to trend down no matter what. (This wouldn't lower costs overall, because in equilibrium, they would be replaced with newly homeless people with higher costs. But this is a cohort study, so those people wouldn't be included here.)