People without both debt and assets aren't paying anything.

Poor people are in debt. They have student loans, medical debt, housing debt, etc.; there are people who owe on houses that they've been long evicted from. Inflation reduces that debt, which is why the fed believes its only mission is to hold inflation down.

People with savings, and who own debt are the people who suffer from inflation. Or would, if there were any. Instead we just have an explosion in price of what rich people already own, like real estate.