I've thought about negative interest rates specifically at length, and I can't imagine a situation where they don't lead to a chaotic breakdown in capital markets or even a currency collapse. The problem is in the compounding: normally there's a negative feedback loop against borrowing too much because you have to pay back more than you borrowed, and if you don't, you go bankrupt and can't borrow any more. With negative rates, there's a positive feedback loop: the more you borrow, the more you make in profit, so everybody is incentivized to borrow as much as they possibly can, nobody wants to pay anything back, total debt increases to infinity, and with it the amount of money in circulation and asset prices also increase to infinity. Additionally, the most profitable sector of the economy becomes borrowing money, so all productive work stops and people focus on financial gains.
This is pretty much the definition of hyperinflation, so there's a template for what happens here, but not in the developed world.
I suspect that a lot of the demand for Bitcoin is also driven by fear of this scenario. In the world above, the incentive for savers is to simply not play in the established financial world; they'll take their savings and put it in assets that are not rapidly going to zero. If only there were a transferrable currency that's deflationary by design and immune to manipulations of supply & interest rates...