There is an incredibly detailed process for exactly that. Called by various names like failure effects analysis, Fault-Hazard Assessment, Failure Effects Modes Analysis, and so on - each has it's own part to contribute to showing problem areas and ways to improve safety.
A complex system of measuring the failures, their effects and ways to make sure they don't happen.
But, like many things, they are done in advance of the real aircraft, and contain assumptions that may not prove to be true in the real world. Sadly.
Considerable effort goes into making and reviewing them for certification - in fact there's a very large Advisory Circular based on this from Part 25 (transport Airplanes) which is used by everyone, including light helicopters.