Blockchain does not care about the price of Bitcoin or what the media is saying about it - it just works and continues to create a new block of transactions every ten minutes. Until it stops, he is alive. It just keeps moving forward, one block at a time, step by step.
I disagree with this thought. The miner mines and gets reward if the reward is worth nothing then he would not mine invest in mining power and other infrastructure. The somewhere or the other way Bitcoin price and the Blockchain mining are interlinked.