Well, one thing is for certain. If a person is homeless, and wanders around alot, then sooner or later he is going to be stopped by the police. And, the poorer he becomes, the more he will be stopped.
The very FIRST thing that a police officer is going to do, upon finding that a homeless man is carrying a handgun, is to confiscate it from him, period end of story. Rightly or wrongly, legal or not, it will be taken and be gone.
What a homeless person needs is something that doesn't appear to constitute much of a threat, and is both effective and quiet, and that role can only be filled by a .22 rifle. I vote for a pump action .22, because it can feed shorts, longs and long rifle, and will function fine with .22 CB rounds (which are pretty darned quiet and can kill small game with ease out to 25 yards.)
The Ruger 10/22, and most other semi-autos, will not fire anything but the .22 LR. So, they are totally impractical.
A lever action would also be fine.
So, I would be looking for a used Remington gamemaster, or one of the newer (Henry model?) bargain priced lever action .22s.
Even less threatening would be a bolt action .22, with a 5 shot magazine carried separately in your pocket, with a good peep sight mounted on it. The older Remington bolt actions, in the 500 series, that were commonly sold in hardware stores when I was a kid, would be perfect for this. (I remember that I wanted the one that was tube fed, and it cost $45. My mom wouldn't buy it for me.)
The rifle should be carried in a sling, over your shoulder, with the muzzle slung down.
By the way, you had better carry it in plain view, because in most states, carrying one of these in a concealed fashion under your coat is a felony (i.e., carrying a concealed weapon.)
Hope this helps the analysis somewhat.
Mannyrock