If they gave somewhere to stay the person then would have a home address. Problem solved, you're welcome ;)
This post was edited by O-uknow at December 28, 2017 8:30 PM MST
Call the American Cancer Society; they might be able to help. Also, talk to social worker at the hospital where his treatment is happening. If they have hotel rooms they may give him access. In my experience if you just keep calling eventually you get some help. Catholic services may be able to help. Call the United Way. Call call call call......
So... maybe open up a PO box for the cancer patient? Most can be done up to look like street addresses these days. You can also have a virtual mailbox.
TM has some good ideas. I also wonder if a homeless shelter can help. There are lots of different types, so finding the right one would depend on location. There is also the option of hitting Craig's List. You never know- someone might actually be willing to take the person in. And, there's the option of Go Fund Me. If someone were to raise funds in the person's name, they could use the money to prepay a room or apartment rental.