Just like gold, in fact, during a recession and bank failures Bitcoin may just perform very well, because it has limited quantity, it is decentralized, and it is relatively decorrelating from traditional financial markets.
Bitcoin is not a "safe heaven" asset like gold. Bitcoin is a volatile and risky asset. The BTC price would most likely collapse just like all stocks prices, if an economic collapse occurs. What economic collapse are you talking about? A collapse caused by a global war or a global natural disaster is different than a recession/depression, which is caused by wrong economic policies. I also believe that it is highly unlikely for a rapid economic collapse to happen nowadays. A slow economic decline, followed by high levels of inflation is more likely to happen in the next few years.
I'm sure that the Bitcoin blockchain is capable of surviving a global economic collapse, even if the Bitcoin price crashes down to levels below 1K USD.