It depends, because different types of assets respond differently to inflation. The wealthier you are, the more likely you are to have more esoteric investments. The bottom 50% of the wealth distribution in most countries (including the United States) own almost no assets (including cash in savings accounts) and are often debtors, so they may find that inflation reduces their debts to a greater degree than their savings.
I think this assumes that wages keep up with inflation, which has not traditionally been the case for low-wage workers (or even high-wage workers for that matter).
