in poor urban areas in the US, are there no small shops catering mostly to immigrants?

I grew up in a city where most of my peers qualified for free or reduced school lunches.

There were no immigrant shops because there were few to no immigrants. None of the major grocery stores were even in the city limits because they were evading city taxes. It was only a 10-15 minute drive, but that requires you to have a car. The smaller local grocery stores in my neighborhood pretty much all closed shop between the 80s & 00s, and they had already been gone from other neighborhoods before then. They were also always more expensive than the larger stores, but, again, those required driving.

There are local stores catering to different immigrant populations where I am now, but there are populationz to support them. They would still require a car to get to.