I think you need to think of your own safety first and not get too involved when helping the homeless, even if the woman was not dangerous she may have been associated with someone who was.

When I lived in Chicago I let a homeless guy live with me for a month (I'm from New Zealand, we have very little homelessness here, I was very shocked by it and wanted to do something) he was a gentle guy, an American Indian, but very messed up, quite a handful, schizophrenic I'd say (I'm bipolar and I'm denfinitly a handful when unwell).

Anyway after a month I needed my own space and asked him to leave, he asked to borrow my coat, then left with it and never came back. I guess he needed it more than me although I was in Chicago in mid-winter without a coat.

Most of my American friends said it could have been a lot worse.