How can poor white people exist when the system was made to benefit them?

[parochial boy]

Basically what Big Abraham and Nathan said. But even then, even in Apartheid South Africa, a system very explicitely and openly designed to priviledge whites, there were still a surprising number of white people living surprisingly precarious existences.

That's the nature of capitalism you see, it creates hierarchies and concentrates power. And a skilled political operator can ensure such a system continues convincing the right class of people that they can only lose from anything that changes.