It is a universal assumption that negative interest rates are impossible. In fact they have a long history. If an economy is in a liquidity trap, and has a negative equilibrium nominal interest rate, then due diligence if nothing else demands that the idea of negative rates be at least examined exhaustively.
Links are below.
An in-depth exploration of negative interest rates concluding they are the solution to a liquidity trap, but at a cost. Willem Buiter and Nikolaos Panigirtzoglou. The best paper LEDR has found on the subject. Three Lessons on Monetary Policy in a Low Inflation Era . Federal Reserve Board.