Not a ton of savings, tbh. You have to eat out every meal, deal with your shit getting stolen, lost sleep, probably lowered social status leading to less desirable jobs. Being poor is expensive.
Nah you don't. I bought an MSR stove that runs off gasoline you can fill up for $.10 at any gas station and then bought bags of rice and lentils that last a week for ~$10. Backpack on back, ask day labor place where to keep backpack when working, employer always had some place to tuck it away. I could earn ~120 / day and only need ~$80 a week to survive. Slept like a baby under my tarp.
If you do day labor all week you just made $500 and you only need $100 to survive the week. Pretty easy to sock money away that way... if you decide to rent a room a couple weeks of that gets you your first week in a weekly rental and from there you can clean up and get a regular factory job. I had a well oiled process that I ran that cycle quite a few times. AFter 1-3 months at a factory I would generally get a fork-lift job or something that paid even more and from there you're basically as rich as the average American.
Bonus: If you have HN skills your average wage from the fork-lift job will give you enough to buy a nice laptop, hi-speed internet and then a high-paying programming job -- although it's obviously not generally applicable (although I've done it).