Wow MP! you did great! Low income is a fact of life. Poor is a state of mind.
I also have to be SUPER frugal with our grocery budget. I've found that buying veggies at the farmer's market is less $$ than the store, we also go to "pick your own" type places, pick a lot and freeze.
As far as chickens, I've found that I can raise mine for about $5 each. I sell 1/2 of them for $10 each, and that pays for all of the chickens, and my family is eating free chicken.
For not having any room to grow anything, I think that most people on a chicken website would have a little bit of room for something, I would think that the poster living in a NYC apartment would be the exception here, not the rule.
I had a friend recently that found out that she could buy vegetable/herb seed on food stamps! that's great!!! I think that would be a wonderful way for some of the lower income folks to help themselves move ahead.
My family is certainly not wealthy, we would prob. qualify for some gov. assistance, but choose not to apply-- we don't qualify for fs, but I *think* we would qualify for WIC, and that's mostly fruit juice--which I don't give my children regularly, milk and cheese--I have lactose intolerant and dairy allergic children, and eggs... so wouldn't be much help to my family anyhow LOL
ETA: also, when having to shop frugally, be sure to shop the perimiter of the supermarket. Most of the middle is junk. Real food is less expensive than packaged junk. Buy a pound of green beans instead of cans, buy flour, oil, sugar and yeast instead of a sack of bread etc... your family and your budget will be healthier for it.