You don't really need to steal food when you can mooch it off other people.
You got me going on this little concept of yours, too lol. I started my own homeless sim. Only thing is that I started earlier. I created a family of 3 with a teenage daughter, put them on the lot, then encouraged the demise of the adults. I then reduced her household funds to $0, and let her have at it. The traits I picked for her were Inappropriate, Kleptomaniac, Mooch, and Virtuoso. I picked Bridgeport, because it just seemed to make more sense that a big city like that would be more likely to have at least some homeless. And I've learned some very interesting things about how the game works.
Kids will always eventually get caught if they're out after curfew.
Always. No exceptions. So sleeping in the park was not an option for my homeless, orphaned teen. Thus, I had to make her home lot suitable to a homeless person:


It's a tiny, 10x10 lot just up the road from The Grind. The weirdest thing about this lot is that it gives her the "Decorated" moodlet when she's there lol.
Also, having to devote most of your day to finding ways to see to your sim's needs like bathing, using the bathroom and feeding themselves, it makes getting good grades in school
very hard. When you couple this with the fact that a park bench was not entirely designed for sleeping on, it makes trying to keep a C average a real task, never mind making the honor roll. Those teenage sims these days just don't realize just how good they have it! So make them finish their autumn salad, because there's a teen in Bridgeport who never knows where her next meal is coming from.

My homeless teen swiped a set of drums and taught herself how to play, and performs for tips in the subway on the weekends. She is probably the richest homeless person I've ever heard of (real or not), but despite the fact that she has well over $100K in the bank, she's apparently stuck on her decrepit little lot. It seems that teens without an adult in the house are unable to move via their cell phones.
I'm finding this to be a real challenge.