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In the approach phase, engine 1 of Cathay Pacific flight 780 got stuck at about 70% N1 and it forced the crew to do an overspeed landing (230knots).

Why didn't they shut it off by turning the fuel pumps off? Is there a backup mechanism if the fuel valve fails like in this scenario?

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You can find the full incident report here and this topic is touched upon briefly, but in short they had little to no time to entertain any other options but a full speed landing.

It was not until the aircraft [was] on the final descent for landing that the Commander realised they could not reduce the thrust on the number 1 engine. The speed was not controllable and from that point, there was no time for the crew to consider other strategy nor procedure to cope with such emergency situation.

and more in the conclusion section...

t. At that stage, there was no time for the flight crew to consider other strategy nor procedure to cope with such emergency situation. The flight crew concentrated on flying the aircraft for a safe landing.

First off, the engine was throwing errors throughout the flight and they were talking to the maintenance team at other points. Ultimately, the proper steps were taken and everything was done by the book. They were prepared for an engine-out landing. When you have a runaway engine malfunction (or throttle stuck at full) shutting down prior to landing may not be the right decision if the running engine provides no immediate safety risk. If you shut down a problematic engine in flight you run the serious risk of not being able to get it started again.

Considering that most airports have a bit (or a lot) of extra runway, EMAS systems and often land at the end of the runway, coming in overspeed and burning through your tires and brakes may be safer than cutting the engine and potentially falling short of the runway.

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    $\begingroup$ Regarding the last paragraph... Any landing you can walk away from, and all that, huh? $\endgroup$
    – T.J.L.
    Jan 22, 2019 at 21:28
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    $\begingroup$ @Joshua - "If you shut down a problematic engine in flight you run the serious risk of not being able to get it started again." - What if you hit a sudden crosswind and have to abort the landing? I'd assume 'doing it by the book' never shuts down an engine that isn't e.g., on fire. $\endgroup$
    – Mazura
    Jan 23, 2019 at 0:35
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    $\begingroup$ @Joshua … and if things are really screwed, you can't be 100% sure you are going to shut down either the engine you intended, or the correct one. We only know this was a "stuck valve because of contaminated fuel" with hindsight. The whole thing could have been caused by an electrical or computer problem, in which case the result of any control action is unknown until you try it and see what happens! $\endgroup$
    – alephzero
    Jan 23, 2019 at 0:58
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    $\begingroup$ @Joshua if you are on a 3 deg glideslope at reference speed with full flaps, if all the thrust is removed you are landing short in the housing development across the highway, unless you are already across the airport boundary, in which case you are landing in the approach lights or maybe if you're lucky you can stretch the glide to the runway and just land really hard. $\endgroup$
    – John K
    Jan 23, 2019 at 1:31
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    $\begingroup$ @Joshua part of the point is that you avoid shutting down an engine unless absolutely necessary - it's safe to do an overspeed landing to a certain point, so why unnecessarily risk? Take British Midland Flight 92 as an example - an engine shed a turbine blade. The crew diverted and shut the engine down. Only they shut the wrong one down, and their actions in doing so just happened to mask the effect (turned off autothrottle, which throttled back the duff engine as well), until they were on approach and throttled back up, which caused a complete failure and a crash just short of the runway. $\endgroup$
    – Moo
    Jan 25, 2019 at 4:43
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Engine #2 wasn't doing its job either

Had the situation just been engine #1 stuck at high thrust, with engine 2 normally controllable, than what you describe would be a reasonable response to the situation. However, that was not the case with CX780 -- during approach, Engine #2 was stuck at 17% N1 (or rather below idle) and thus delivering effectively nil thrust.

As a result, the pilots dared not shut down engine #1 until they were safely stopped on the ground.

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    $\begingroup$ All this talk of engine #1 and #2 I assumed that #3 and #4 were functioning normally for quite a while whilst reading here. $\endgroup$
    – Flexo
    Jan 24, 2019 at 17:51
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    $\begingroup$ @Flexo -- nope, only two engines to be had here! $\endgroup$
    – UnrecognizedFallingObject
    Jan 24, 2019 at 23:37
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    $\begingroup$ @Flexo By #3 and #4 you mean the pilots taking paddles and paddling the air through an open cockpit window? :) $\endgroup$
    – yo'
    Jan 26, 2019 at 14:13
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    $\begingroup$ @Flexo: Alas, 'twas an A330, not an A340. $\endgroup$
    – Vikki
    Sep 10, 2019 at 4:26
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From the incident report section 1.1.4:

a. At 0519 hrs during the descent to a cleared level of FL230, ECAM messages “ENG 1 CTL SYS FAULT” and “ENG 2 STALL” were annunciated within a short period of time. According to the Commander, a light “pop” sound was heard and some “ozone” and “burning” smell was detected shortly before the ECAM message “ENG 2 STALL”

Then later:

e. At 0530 hrs, when the aircraft was approximately 45 nm southeast from VHHH and was about to level off at 8,000 ft AMSL, ECAM message “ENG 1 STALL” was annunciated.

So now both engines are out, they started the APU and successfully managed to restart #1:

h. The crew moved the thrust levers to check the engine control but there was no direct response from the engines. The No. 1 engine speed eventually increased to about 74% N1 with the No. 1 thrust lever in the CLB (climb) detent position. The No. 2 engine speed remained at sub-idle about 17% N1, with the No. 2 t hrust lever at the IDLE position.

Engine 2 was out of action, producing no power, engine 1 had failed, but was temporarily working although they couldn't adjust power, if they'd shut that down too they'd have been gliding and probably would have crashed with total loss of life. They didn't have the power to climb and had one shot at landing, so they made damn sure they got it on the runway, not a bad landing considering the circumstances.

On a humorous note, another example of pilot understatement:

l. At 0539 hrs, the Commander made another PA advising the passengers of having “small problem with the engines” with small vibrations and requesting them to remain seated and follow the directions from the cabin crew.

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    $\begingroup$ It's only a "small problem" unless the engine is completely missing. $\endgroup$
    – Jacob Krall
    Jan 24, 2019 at 15:26
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    $\begingroup$ To be fair, he was technically correct. The actual problem was microscopic... $\endgroup$
    – TemporalWolf
    Jan 24, 2019 at 20:45
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    $\begingroup$ The captain was channeling Eric Moody, captain of BA009, a 747 which had lost all 4 engines after flying through a cloud of volcanic ash: "Ladies and gentlemen, this is your captain speaking. We have a small problem. All four engines have stopped. We are doing our damnedest to get them going again. I trust you are not in too much distress.” They got just enough engine power to get to Jakarta. $\endgroup$
    – GdD
    Jan 25, 2019 at 12:32
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    $\begingroup$ Was any explanation given why both engines were malfunctioning at the same time? $\endgroup$
    – Faheem Mitha
    Jan 25, 2019 at 13:43
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    $\begingroup$ Yes @FaheemMitha, the fuel delivery system at the departure airport had gotten contaminated with salt water, this had caused the fuel filter material to gel and turn into tiny spheres. These spheres gummed up the fuel management valves in the engines to the point where they seized up. #2 seized on idle, #1 finally seized on 70% throttle, which is why they couldn't change the throttle settings. $\endgroup$
    – GdD
    Jan 25, 2019 at 13:48
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Aside from what Unrec. and GdD point out, even if the other engine had been running perfectly...

A frequent problem with twin engine airplanes is shutting down the wrong engine. Nobody ever expects or plans to shut down the wrong engine, but it happens anyway.

So a crew is very cautious to shutdown an engine that is working.

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    $\begingroup$ A fascinating point. $\endgroup$
    – Fattie
    Jan 25, 2019 at 10:59
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    $\begingroup$ You can find videos on youtube where crews rehearse engine failure situations. There's all kinds of confirming related to shutting down an engine in flight, for good reasons as @harper stated above. $\endgroup$
    – Jpe61
    Sep 9, 2019 at 18:33
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I could be wrong but reverse thrust from the running engine helped to stop the plane1 as it was approaching at a great speed way over the recommended landing speed, so shutting the running engine off right at approach would have made the plane to overshoot the runway, making the situation worse.

1: Source:

[...] The aircraft then rolled left seven degrees and pitched down to -2.5 degrees at the second touchdown during which, the lower cowling of No. 1 engine contacted the runway surface. Spoilers deployed automatically. Both engine thrust reversers were selected by the Commander. Only No. 1 engine thrust reverser was deployed successfully and ECAM message “ENG 2 REV FAULT” was annunciated. Maximum manual braking was applied. ... [Accident report, page 26. Engine #1 was the one that was stuck at 74% N1.]

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