What happens if precautionary savings increase across the board?

The COVID crisis may trigger a widespread increase in precautionary savings among households and companies, due to the increase in uncertainty (health, economic) and the increase in public debt. What happens if precautionary savings increase across the board? Demand will obviously be depressed; Fiscal and monetary policies will remain expansionary; Equilibrium real interest rates will become very negative; The decoupling between asset prices and the real economy will be further amplified .