Wealthy people hold investments that make let's say 7% a year, while working class people make $x a year that grows probably much less than 7% a year. So if inflation is higher, wealth inequality grows less quickly, or in some cases can shrink, as was the case after the world war, because Europe was destroyed so inflation was rampant which actually created a lot more equality. Same thing happened after the Black Death in Europe. It's painful in the short term but can help reduce wealth inequality. Also I wonder if people on a fixed income like social security might be able to stave off the effects of this if social security grew at inflation.

Thomas Piketty's book capital is a great source for this^