That money sits... forever? Prices don't respond to money being removed?

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.

Savings would be invested significantly less with a fixed money supply, because every possible alternative investment is statistically guaranteed to have a lower expected value than simply holding onto your money. Obviously, there are still going to be people who attempt to beat the market. But it will happen significantly less often since the "default" of holding onto your money is both the safest possible investment and the most optimal.

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.