Proponents of modern monetary theory have come up with their own idiosyncratic definition of savings in support of their theory. But the common usage of the term shows MMT doesn't work the way its supporters think it does.
Keynes viewed depressions as something that could naturally plague market economies when total spending was insufficient to support full employment. Only with wise oversight could we hope to achieve steady economic growth.
The new Keynesian recommendation for monetary policy is to “stabilize the growth of aggregate demand.” In plain language this means that the monetary authorities should never stop flooding the economy with paper money.