but that sure sounds like a case where avionics decide that keeping that engine running is a major threat and shut it down without human intervention. Looking forward to reading input from people who know whether that's even possible...
No idea about the type/engine in question here, but for example on a twin you'd need to be darned sure your automation ensured you didn't shut down a sick but running engine/thrust producing engine (e.g. due to low or zero oil pressure) without checking the state of the other engine first.