Chain Death Spiral happens if BTC loses virtually all its miners.

Generally, the BCH:BTC hash share is roughly the same as the price ratio (block reward ratio to be more precise). Now it's 0.095:1.0, and BCH has around 9%. At price parity BCH would have 50%.

However, if the BCH price suddenly rose hugely - say tenfold - (eg way above 1.0) during a BTC difficulty period, BCH can theoretically take all of the hashpower until the next BTC difficulty adjustment (which would never happen...). However, even during EDA madness around 30% of miners stayed with BTC even though it was less profitable to do so.

Chain death spiral is extremely unlikely.