[slightlyovertaxed]

Probably locally grown or they gravitated to a big city before the disease completely took them down. Remember that schizophrenia tends to strike in adulthood. You may have a regular guy who, in his 20's, completely falls apart.

In NYC and other major cities, it may be that they're shipped in from surrounding areas into a jail or hospital for temporary treatment, then dumped onto the street. Also, think of it in terms of poverty and population density:

NYC is one of the most expensive cities in the world. However, if you go away from the middle, you are in the ghetto where there aren't as many services and a massive population. The combination makes it likely that you have homeless, locally-grown people who spread throughout the city by jumping turnstiles and riding the subways. It's warm down there, people are always throwing out food, and the police tend to turn a blind eye unless things get violent.

[slightlyovertaxed]

FYI, this is something that I’ve studied and read about. If you want to know more, read the book “Crazy”. It’s written by a guy who watched his bipolar, delusional son go through the Miami-Dade prison and mental health care system. It’s a good, if somewhat dramatic, read that shows how screwed up everything can get.