There are also utility deposits, auto insurance, etc. But, there are a tremendous amount of free resources available to poor people, from food stamps and food kitchens to clothing. It could be easier for someone with nothing to scrape together a few thousand bucks than someone in the middle class. If your food is subsidized, your income tax rate is low, and your lifestyle costs are low, e.g. not having to insure a home or expensive car, then you should be able to save quickly.
So, I'd assert that: Impulsive people, those severely uneducated in their economic alternatives, or those with little marketable skills stay poor because they continue to make bad decisions.