Firstly, it is very rare for this to happen. The closest experience I have had to it was 1987. The market had been severely overheated for quite some time. So, we should have been only lightly exposed to the market - and I was, with only about 25% of my funds in the market.
On the day of the crash, every stock I held went below its stop-loss at the open. Moreover, the spread on some of them was several dollars and on others there was no bid at all.
You are right - you do not panic. Instead you do what I did - sell into the first rally. It was the next day and I sold the lot. A stop-loss is inviolate. If you hesitate to take it, you are breaking the cardinal rule of investing and trading. Your stop-loss is where you are wrong about your trade. If you are wrong, you have no business staying in the trade.
Sure, sometimes in hindsight you would have been better off to hold on. The problem is that you cannot trade in hindsight.
One interesting insight from Jack Schwager's latest book is how many of his "wizards" abhor unruly markets. They get out and wait until order is restored and then trade orderly markets.