Miles Kimball has promoted his system of defining the dollar in terms of electronic money and allowing hand-to-hand currency to float during deep recessions.
He argues that this would allow nominal interest rates to fall below zero when necessary. Interestingly, he also argues that this possibilities makes it possible to create truly "honest money" with a zero inflation rate rather than the planned 2% inflation common among central banks today.
In my view, banks already issue "electronic money" and there is no need to have the Federal Reserve provide start providing it directly to the public.
The Fed already provides "electronic" base money to the banks, and that is enough. Let reserve deposits at the Fed "define the dollar" though ordinary bank deposits would be redeemable in that base money and so reinforce that definition for other firms and households.
And what about currency? Rather than try to have the Fed manipulate an exchange rate between government currency and deposits, simply get rid of the government currency and let private banks issue the currency. Normally, that currency would be redeemable in reserve balances at the Fed and the privately-issued "electronic" deposits created by banks.
If there is a "national economic emergency," and extremely low interest rates make it attractive for households and firms to hoard currency and profitable for banks to issue less currency, then the banks will stop issuing it and there will be a currency shortage.
Meanwhile, market interest rates on various securities, including "electronic money" could adjust to clear markets and keep spending on output growing at a slow steady rate. The most likely consequence would be that interest rates would never actually fall so low, and there would never be a shortage of currency. The second most likely scenario would be that any such currency shortage would be very short lived. Disruptive, but not much of a problem.
But finally, if market clearing interest rates on deposts are presistently so negative that a shortage of currency persists, then let the private sector come up with solutions. Perhaps ordinary retailers would issue dated script--more like coupons than what we now think of as currency for these small, face-to-face transactions.
Suppose tax evaders and black marketeers start using private gold coins for their transactions and to store their wealth. So? The price of gold would change with its supply and demand, just as today. Let it.