I see this mentioned often, but it just isn't the case. In order to effectively implement negative interest rates, we will have to modify the exchange rate between physical cash and bank deposits to remove the incentive to hoard physical cash above the amounts needed for normal daily activity, but we will not need to ban it outright. This paper[0] from the International Monetary Fund explains in more detail the steps banks will take to implement the changes.
Whoa, the guys who wrote this paper should get treatment not dissimilar as people who helped design and build Nazi death camps.
People will just ditch banks and return to exchanging physical currency in their transactions. Why would you need electronic money if it incurs additional fees?
[0] http://www.imf.org/external/pubs/ft/wp/2015/wp15224.pdf