Kaede is running for her life.
Don't get her wrong, if she gets caught she's probably not really gonna die. They'll probably just give her a beating and take her food from her. But they do have some rather large blades and if they want to they can rather definitely get her killed with prefect impunity; the Chou brothers are, after all, above the law. Or they're the law. One of those.
Still, they have food, and her people don't, so she steals from them to help her people. That's just the way it is. It's unsustainable, and it's unfair. She has plans. But while her plans aren't ready to see the light of day, she steals, and she runs. That's the status quo.