In the post-war period, deep recessions (of the sort that might, in extreme cases, call for negative real rates) have typically been preceded by periods of strong inflation pressures. These pressures resulted in significant economic distortions, which, in turn, affected the depth of the subsequent downturn. In the absence of such inflationary distortions, the downturns are likely to be much milder.
Hence, there is less likelihood that a period of negative real interest rates would ever be called for. Moreover, while nominal short-term interest rates cannot be less than zero, it is worth underlining that a near-zero nominal rate will still imply a real interest rate that is appreciably below its equilibrium value and will provide considerable stimulus to the economy.