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.
This question is not appropriate because Bitcoin was created and has proven itself in the midst of extraordinary economic problems that made people distrust the existing system at that time and until now Bitcoin still holds its value unchanged. What people fear about economic collapse is the decline in the value of the currency and again I say Bitcoin is able to maintain that which we call the best hedge.