What do you mean by, "actively being used" though? The rich tend to want a return on their money, "invested" seems like a type of use, even if it is passive. Crazy hypothetically, if it reduced the money available for investment, it might raise the interest rate on loans, reducing the rate of lending, so reducing the total money supply.
I'm not sure that the rich usually invest in terms of making loans available, so I don't think your concern will happen. What might happen is a decrease in investment, which might lead to a decrease in economic growth. (Or, alternately, to a decrease in the rate of installation of automation, which might preserves jobs...)
