What happens to interest rates when they are already at (near) zero and the stock market crashes? Let's say the global stock market crashes in the coming months (it's currently at an all time high in the western world). What happens to interest rates?

"Usually", as I understand from my absolute layperson perspective, interest rates would be lowered as a counter measure. But what happens if interest rates are already (nearly) zero, as is the case in some countries?
They would be just pushed to their lowest possible level. Recent experience in Switzerland and Germany shows the interest rate can be slightly negative but that’s it. Once the interest rate hit (zero) lower bound it can’t be pushed further as long as there is cash that carries implied zero interest. At that point central bank would have to resort to other policy instruments such as QE, helicopter money, forward guidance etc.

However, if some western country would decide to go completely cashless it would be possible to have arbitrary negative interest rate. In that case the interest rate would just get pushed further down.