More importantly you should have read the article until the end. It mentions that the program pays for itself. In other words, the government spends less by providing this housing to the homeless, because the savings due to medical/emergency services are _larger_ than the costs of providing the housing.

From a pure money perspective, it sounds like they cost less to society when they are provided housing, so your concern is somewhat moot if you only look at the monetary side of things (which is, I believe, the angle you were concerned about).