Let's say you had one backpack for storing food.
No microwave. No stove. No fire. Trip to the grocery store...what do you get?
Remember, there's only a backpack for storing food.
It has to be dirt cheap, but you want to stay healthy. Is it possible? What would you eat?
I'd then consider going freegan and eating whatever the grocery store is throwing out, that I don't subsequently have to cook.
This is a fun question but only because it's pretend. My family lived in our car one summer and that wasn't so fun. My dad, bless his heart, would buy huge packages of sandwich cookies and I hate them to this day. We called them "shipping cookies" because he bought them for every long trip since they were dirt cheap.
On the other hand, we roasted hot dogs on long sticks in firepits at the park and I was too young to realize we were desperate so that was great fun.
Now, if I could afford it I would load my backpack with all the things I have to limit because they are too dense--nuts, dried fruit, jerky and meat sticks/sausage, along with some carrots and fruits that can take squeezing such as a grapefruit. I assume I'd spend the day walking around so I could burn up those rich foods.
If I couldn't afford the above I'd have to walk around the supermarket and select foods in a compromise of money vs. paleo vs. weight/volume.
Canned fish - sardines. This is what I typically eat when I'm out & about & get hungry. A tin is like 99 cents and full of good things (skin and bones). I know there's an issue w/ BPA in most tins, but it's possible to get clean cans.
I think a combination dumpster diving, foraging, buying food from a store and trying to get food from the food bank would sustain you. I'm definitely not above dumpster diving. I think having the tools you need to catch/collect/cook food in your pack would be better than filling the pack with food. I would get a bag of jerky, canned sardines and a jar of coconut oil (or ghee if coconut oil was too expensive) to give me the energy I needed to get my hunt and gather on. Butter, even in winter, might not last in NC due to warmer weather. I think I would try to avoid eating squirrels, pigeons and raccoon because of their diseases and parasites.
Here's a quick list of foods off the top of my head I could eat in my area, that I can already easily recognize, gather/catch and know how to prepare. I live in North Carolina.
Spring + Summer:
Fall + Winter
I've always said that nuts and nut butter would be my choice in this situation. You get the most bang for your buck when it comes to overall "healthy" calories per serving.