Most low income working people I know avoid debt like the plague - with the exception of car loans and house loans, which low and middle income people pretty much approach the same way, but just purchasing at varying price levels.
Just to be clear, I'm comparing low and middle income families. That said, low income people do spend a larger percentage of their money on food and energy as compared to middle income families (since everyone needs to feed themselves, keep themselves warm and go places).
I think students would be the only exception to this...but I'd guess they're an exception, as they are taking out debt because they know their future earnings are going to go up in the long run.
Edit: However I do see what you're saying in terms of upper income people losing money tied to investments due to inflation. But I'm just saying, all else equal, for a zero-debt lower income household vs a zero-debt middle income household (of which there exist many), the lower one is going to get hit hard by this.