These are multi redundant and generally hospital patient monitoring systems have additional batteries of their own to make sure people don't die, and in the case of a major clusterfuck there are emergency procedures in which it's specified how power will be restored assuming a grid and backup generator failure (usually it involves the fire department shuttling a generator pack to the hospital site).

With engine failures in aircraft however, the consequences can be way more dire - particularly in GA where it's (at least in the US) even being allowed to fly without a license at all (Part 103 ultralights), and forget about regular legit simulator training on what to do in that case.