Check out this NY Times Article.
http://www.nytimes.com/2013/03/18/ny...s&emc=rss&_r=0
While NYS on the book certainly does guarantee shelter, all that does is guarantee a place in the shelter system. Bloomberg has said fewer people are leaving the system because the state of New York cut funding to a HRA rental subsidy program. Just because you enter the shelter system DOES NOT MEAN you will get an apartment.
If the case workers determine a person is from another place and has family who can accomodate them, they are purchased an one way ticket out of town. Thousands have been sent out of town since 2007.
Now of course, lets see how the House Republicans actions affect all this, as they butcher the budget for certain things.