If the world's electricity goes out, Bitcoin could still technically survive as long as at least one blockchain server is running and accessible. This means that if there's a way to keep even a single node online (using alternative energy sources, for example), the Bitcoin network can continue to function. However, it's not just about electricity. Bitcoin also relies on global networks and the internet for transactions and communication. So, if the entire internet goes down, Bitcoin would lose a significant portion of its functionality.
In a nutshell, Bitcoin's survival in a total power outage hinges on keeping at least one node operational and maintaining some form of internet connectivity. It's a resilient system but not completely invincible to global-scale disruptions.