The only 'saved money actually doing nothing' scenario I can think if is when it gets deposited in a bank who then turns around and hold those funds at the cent

The only 'saved money actually doing nothing' scenario I can think if is when it gets deposited in a bank who then turns around and hold those funds at the central bank because they have nothing else to do with it. Central banks in many currencies these days offer negative deposit rates to discourage that behaviour and thus to the extent it happens it tends to only be over a very short period of time. Of course it doesn't mean that investors/banks who receive the money reinvest it in the same country - if there is a dearth of opportunities in eg the US and Europe then this type of activity may result in increased investment in emerging markets.