But with deflation, the cost of eating goes down so the poor can save more.
No, the salaries go down as well. Zero-sum game. If you never get the chance to save, you'll never profit from price deflation (or at least less than the wealthy).
The reality is that inflation hurts the poor the most and helps the rich. Most of the wealth held by wealthy people is in the form of assets such as real estate and companies. Poor people hold most of their wealth in cash. Inflation helps wealthy people at the expense of poor people because the values of assets go up and the value of cash goes down.
Wealthy people such as bankers and politicians love inflation.
I agree that price inflation hurts the poor more than the wealthy. But so does price deflation.
But I think we're getting off-topic here. There are a lot of threads around discussing the good and the ugly of inflation and deflation. I suggest we stop at this point and keep discussing the OP