I think you may be referring to the newer philosophy on reducing chronic homelessness in the U.S. that has been shown to be quite effective and is endorsed by HUD and other housing programs. It's called Housing First and is based on the premise that when individuals are given stable housing that isn't contingent on other conditions, the rate of chronic homelessness can be reduced long term. And yes, it is more cost effective. (No worries, I read tons of reports/articles/interviews and can't recall all of them either).
The program is counter-intuitive to the typical belief that a "non-productive" member of society (and for the record, I don't agree with that premise, everyone is unique and contributions are measured in many ways) will remain non-productive if given housing and other supports. What the program has found is that stable housing is the catalyst for many people getting off the streets and re-entering society. Is it perfect? No, but no rehabilitation/human service model is but it is being in more and more major cities because the results have been positive. It has been in effect in the city where I live for many years.
I have worked with homeless people and I rarely ran into someone who just wanted to take from the system (unless they were using and not able to deal with their problems or reality at that time)...they all talked about work, their families and even helping others. Some of the chronically mentally ill who were dealing with severe delusions or paranoia had difficulty being in shelters (fear, violence, past traumas) and preferred the streets.
And I'm not saying there aren't some percentage "gaming" the system but it is small in comparison to the people who truly need and benefit from the services, whether housing or health care.
FWIW, Obama phones are a myth...I have worked with people that have this service and the program exists through the FCC and was in effect before Obama became president.