This happens because the poor continue to transact hand to mouth and are unable to save while the wealthy accreted value on their idle cash. Invested cash creates economic activity. The cash in your mattress does not. The opposite is true in a deflationary environment.
Debt in an inflationary environment benefits the debtor, as the loans are denominated in the dollars at the time of loan issuance. To the extent that the economy grows faster than your debt load you do not in fact ever have to pay it off.