I am curious if we're entering a period where western governments must run deficits and central banks must purchase said debt at sub zero interest rates to keep the economy running.

In principal this could occur if there were large capital “sinks” in the economy where paper money is being removed from circulation or it's velocity plummets. This could occur if for instance certain economic actors could acquire large cash flows that they then deposit into illiquid non productive assets.

E.g. Housing, universities, Large rent speaking corporations with offshore accounts, individuals with the same.