Okay, so I took my concerns to my supervisor and other teachers to get an idea of how things like this are handled, and basically what I got was "Do Nothing."
Most people who spend a lot of time sleeping on the street and in various states of undress are considered to be mentally ill. If their families cannot take care of them, there is nowhere for them to go until they become a hazard to themselves or others. Then they go to prison, where they either improve or die. Although Peru seems to have socialized medicine and is actually quite advanced in their medicine, there is no long-term care for anyone unless some money is provided. There is no state funding or social security of any kind (that I can find out about) for poor people with chronic mental illness. There isn't even a state mental institution. So the treatment for poor, mentally ill people in Lima is to turn them into the streets and ignore or avoid them until they die or commit a crime. Street vendors feed them when they can, and their diet consists of whatever the vendors can spare - soda, candy bars, and potato chips usually. I don't know where they go when it gets cold, but I imagine I'll find out one of these days.
These are not good answers for me, but I don't know what I can do to make things change. I hope someone will read this and tell me that I'm mistaken here. I hope they'll tell that there really is someplace that people can get treatment when they are at their worst and have hit rock bottom.