My interpretation of malfunction is that the engine has completely failed or it is producing partial power.
I see it differently. If there is function, there is something. Maybe enough engine power to climb away, maybe not, but factor which the pilot will have to consider to best choose the next action. If the engine has failed, and is not producing anything like flight power, I don't think many pilots would then think of that engine as still "functioning". For the purpose of powered flight, it has failed.
As has been said, with the narrow exception of undoing a wrong pilot action which may have caused a failure of the engine to produce useful flight power (like selecting tank with fuel in it again/selecting the mixture to rich again, or returning the throttle/power lever to the "power" position again - I'm thinking of some recent King Air accidents for that one), most anything else I can think of is not likely something that most pilots will get dependably resolved before the opportunity for a good forces landing has passed. A good forced landing is more important than allowing that opportunity to pass, and doing a really bad power off return to earth. So, if the engine has failed, and super simple prompt action won't fix it, do not make any further attempt for that engine to produce power (in a single engined airplane), and devote all of your attention to a decent forced landing. Close the throttle, so you are not distracted by an engine which fools you with one last gasp.
If, on the other hand, the engine is malfunctioning - it is still functioning - different scenario! We're not going to needlessly waste a plane, and get it into the news slid into a schoolyard, we're going to assess. Maybe it's an emergency, maybe not. So a mag quits, and it runs a little rough, continue the flight such that a further failure ('cause then it'll actually be a failure) will have the lowest risk - circle back safely for a reasonably normal landing, making the best effort to not need to overshoot.
I am unconcerned about the fine nuances of picking fly poop out of the pepper to arrive at the perfect emergency brief to satisfy a very particular situation or examiner. I am interested that a pilot would give thought to what actions will be done from memory during the initial phases of departure, to minimize risk. If that is happening, excellent! If it's not perfect, it's like everything else in aviation, we do our best, and try to do even better next time. Posts with passion here are good. What's really good is all the pilots reading this, who may choose to not jump into the discussion, yet are rolling all these points over in their minds, and expanding their thinking as a result - that's the benefit here!