From what I've read, poverty definitely leads to lifestyles where you're "trapped" in poverty for a long time, or forever. It's like the disability we have in the US: once you're on it, you're very unlikely to ever get off it.
However, it's not just poverty that's the issue. It's mental health, it's drug abuse, and the lack of paths to a sustainable (long-term) lifestyle for these people who are homeless.
That means education: how to manage your money, what's a "good deal" involving various things, and how to take care of yourself.
It's incredibly surprising how many of these people get taken advantage of.
If you have close-to-or-zero skills, how can you possibly sustain yourself? If you have skills but you cannot recognize (because you were never taught) when you're being taken advantage of, how is that sustainable?