I think there is one in Healer? 🧐

The elevator is "Happiness' is a character of its own. While it's not 'faulty' but initially the residents are warned against riding it, and then the scene where Ji Hyun tries to stop the zombies from getting into the elevator and then gets pulled in to safety by Sae Bom at the last minute is K-drama gold.

Healer (ep 8): elevator fall down
Big Mouth (ep 7): Mi-ho attacked while stuck in elevator
Liar Game (ep 10): elevator fall down
Start-Up (ep 15): stuck in broken-down elevator
Touch Your Heart (ep 6): Jung-rok and Jin-shim stuck in elevator
Bad and Crazy (ep 10): elevator stuck halfway-down

I would like to suggest a hunt for my following ideas:
(1) real-life Filipino actors and actresses on Kdramas
(2) exploding cars, trucks or any other vehicles
(3) crying in the rain or in the snow
(4) people who getting pantsed
(5) Kopiko PPLs or any kind of real life coffee/coffee-related PPLs (e.g. Starbucks, Nescafe)
(6) breaking plates, glasses or any other utensils

Secret Garden:
Somewhere in Ep 14/15, she rides the elevator in his body while the shady Secretary stalls the elevator. Then Secretary runs off once he knows he had been caught in the act. And that exact moment the body switch happens and he ends up in the elevator is his own body and his claustrophobia kicks it. It was quite an intense scene 🙃

True Beauty : The scene was hilarious with the FL who needed to pee and the ML who offered her a bottle 🤣

Que Sera Sera : The cutest first kiss scene :p

I remember the already mentioned intense scene in Secret Garden, but apart from that... I can only think of crowded elevators (everywhere) or magic elevators (as in Scripting your Destiny).

And the only faulty elevator scene which comes to my mind is from a C-drama: Meteor Garden.

He Is Psychometric (episode 1)

Jin-young (ML) is saved by Jo Byeong-kyu from an elevator in a building on fire. ML's parents are still trapped in the elevator as it falls down.

I would say Uncanny Counter 2 (episode 2) had a faulty elevator in as much as Jin Seon-kyu's character's wife was killed.

The secret life of my secretary. Towards the end. I don’t remember exactly what happens but the lead gets stuck in an elevator, has to be rescued out, and runs to the female lead. He has some PTSD as well. I just remember that it was emotionally jarring for me.

Just Between Lovers
The FL was scared of elevators and used stairs.

Well, nothing bad happened but about a hundred-ninety conversations took place in and especially in front of elevators in Phoenix, they must have saved a ton on sets.

Oh my gosh... my very favorite example of this is a funny version of the scenario in The Sound of Your Heart (the original, not the remake). The ML and FL get "trapped" in a "faulty" elevator, and completely spiral into chaos, before realizing . . . (*SPOILER*) . . . they never pressed the button 😂

Since HAPPINESS was already mentioned, here's my another favorite faulty elevator scene - QUEEN IN HYUN'S MAN, Ep3-4 (ending scene of 3, beginning of 4). While the elevator itself was working properly, CCTV inside it wasn't, allowing FL to go along with them feels and jump-kiss totally unprepared for such boldness Joseon time-traveller ML without sacrificing her innocent reputation as a celebrity. The best part? She didn't know atm that CCTV was off but went for it anyway)))

Not a kdrama but in Taiwanese drama Love Around, they get stuck in a faulty elevator - I think he offers to hold her hand if she’s scared or something else fairly innocuous and she overreacts like crazy 😅

Radiant Office, episode 3: Elevator stop leads to one of Ho-won's fantasy thought sequences.

There is a falling elevator in My holo love (one of the numerous similarities with Healer).
And Ji Chang Wook also meet an elevator of doom in the K2.

Help me here - wasn’t there a wonderfully funny scene early on in The Rooftop Prince where he and his followers thought the elevator was the place to get changed? But then the doors opened in front of a crowd waiting to get on? That elevator certainly didn’t work as expected! 😂

in "sweet home" the elevator works fine but ends up being the place of the saddest death in the show. because the elevator worked so damn perfectly, a monster just shuffles in and breaks our hearts.

does this count? LOL

Touch Your Heart, Episode 6, has a faulty elevator leading to much URST. And then there is gossip the next day that a couple were sprung kissing in the elevator when it got stuck- so our leads are going around being guilty and furtive when all they actually did was gaze at each other!
She Was Pretty has a stuck elevator in episode two ( or maybe one? near the beginning). FL is anxious because hiding her identity from ML.. but of course ML thinks she is anxious from claustrophobia. Either way, he is kind to her- which is just as well, because the is then awful to her for the next 4 episodes.