If you sit on money you get from the economy, you are taking it out of the exchange system as long as you don't spend it, which slows exchange.
Savings would still be invested with a fixed money supply, because investment provides a return whether nominal prices are falling or rising.
Sound investments will account for either inflationary or deflationary trends, just as they do now.
This is clearly the case when nominal prices are falling. But when prices are rising, the reason they are rising is a contraction of the economy… and again, your money is still best left alone. Because while your investments might pay off when the economy rebounds, you'd still be statistically better off with your money sitting under the digital equivalent of your mattress; when the economy rebounds, prices will fall again, and your untouched money will be worth more in direct proportion to how much the economy has rebounded.
With USD, you know the value of your currency will drop due to inflation. In order to keep up with inflation, you have to put your money in an investment vehicle that stands in as a proxy for the overall economy. Hypothetically, you could buy a perfectly proportional amount of every single listed stock, every bond, piece of real estate, and so on (this is what index funds attempt to approximate).
In the latter example, you also have managed to convert your currency into an ideal proxy for the entire economy. Any attempt to pick winners or losers will, statistically, give you slightly worse results on average than had you simply tracked the market as a whole.
Both examples are similar, except in the latter example, you've actually put your money back into the economy: a company issued the stock in order to raise the capital to expand and grow. In the former, your money is essentially removed from the overall money supply. It is available to no-one, and causes further deflation. The more money you hoard, the less money available for financial transactions. The less money available for transactions, the more valuable each unit of currency becomes.