Actually, in first world, not even an homeless gain less than 2$ per day.
So we can safely leave all the expenses for fuel and cookware out of the math.
If you think there aren't homeless people (and others) who don't gain any money at all, you are living in a fantasy world.
Some don't get $2, not even $1. Some are lucky to get $0 instead of losing money every day.
Sure, some homeless people get assistance from public or private sources, but many others are too mentally ill, depressed, or self-destructive to seek, find, or even accept aid (when aid is available, which it not always is).
And yes, these people do die of starvation, exposure, malnutition, illness, suicide, drug overdose, etc..
Sure, if you're depressed or otherwise crippled, you can earn nothing. But I assume $2 is still about 200 beer cans at Reynolds Aluminum Recycling in the US, right?
The extreme poor area I lived in was also full of drug addicts who spent all night going through trash bins and cleaning out anything of value to support their habit, so if your plan is to mine for recycled bottles and cans to return then you're in for a surprise when you find out that hustle has already been cornered by violent drug addicts and alcoholics who won't let you near their garbage 'turf'.
They also rob each other when they walk out of the recycling depot with cash in their pocket. Since you live in an alley you don't have security
They do move around, and are typically arrested and ticketed by police for doing so. If you were to move to a suburban area a resident would complain about the hobo pushing a shopping cart and squatting in the woods so you would find yourself being given a "starlight tour" which is when the police drive you to the middle of nowhere and kick you out of the vehicle at 2:00am.
Obviously is not a simple life. Dangers are everywhere from drug dealers to policeman.
But to keep this short the fact is the same: For a mentally sane man (or woman) in USA is very difficult die of starvation.
