New York hasn't gotten rid of homeless shelters. There's a big one on Ward's Island in the middle of the city. However, it's a bit... isolated. If you want to get there on foot, there's only one footbridge, which is never open after 8:00 PM and not open at all in fall and winter.
There's another way to get there: take the M35 bus from Spanish Harlem. It's quick -- ten minutes or so. But it is a city bus. And if the homeless, destitute people who need to take this trip can't muster the $2.00 fare -- every single night -- the city has also provided cops to arrest them.