Chronically homeless people (those spending weeks and longer on the streets, maybe 10% of the total homeless population) present a significant financial burden on their fellow citizens. They have vastly disproportionate medical expenses (more frequent and more complex illnesses) and higher policing expenses, paid for by the taxpayer. The taxpayer may also choose to donate money to charities helping homeless people (or other charities that indirectly give money to this cause).
In Denver, the powers that be have found that the total financial burden borne by its citizens can be reduced by offering chronically homeless people a rent-free apartment and a dedicated case worker to try to get them on their feet. It is often impossible to turn these people's lives around, with the challenges this section of society face; nevertheless, housing them indefinitely, for life if needs be, is cheaper than pumping money into public services, either through taxation or by charitable work.
An article for reference: Million Dollar Murray
If your lifetime economic burden was reduced, would you allow your local council to build housing and give them for free to the chronically homeless? Economically, this makes complete sense. Ethically, it's tricky - why should a homeless person get free housing when many of us can't afford our own?
So, morals or money?