If there's a crash, people would sell Bitcoin and stocks to cover other needs.
We've seen already Bitcoin falling just before the stocks have fallen too. Many use Bitcoin in a similar way to stocks.
Maybe I'm wrong. I hope so. But.. what if I'm right?
Stocks are nothing more than an investment tool. Bitcoin is a multifunctional tool, and is something that you don't necessarily need to convert to fiat in order to sustain yourself. If merchant adoption picks up in the forthcoming years, and that will very likely happen with LN, people are able to conveniently do grocery shopping, pay bills with Bitcoin, etc. The difference between Bitcoin as investment tool and a currency tool won't endlessly remain as massive as it might be right now. Stability, or something close to that will do miracles. It takes time, I know, but everything takes time in the end.
At some point there will be a time where you have to pay a nasty, like really nasty premium in order to convince people to sell their coins to you for fiat.