휴대폰이 꺼지는 바람에 네 전화를 못 받았어

The line, explained

Every relationship in a K-drama eventually hits the missed call. Someone waited, someone did not pick up, and the next scene opens with an apology. Korean has a pattern tailor-made for that apology: -는 바람에, 'because something unexpected happened'. It does two jobs at once. It gives a reason, and it signals that the result was unwanted, so the speaker is not just explaining but asking to be forgiven. Today's line is that apology in its classic form.

휴대폰이 is 휴대폰, 'mobile phone', plus the subject marker 이. You will also hear 핸드폰 and simply 폰, all meaning the same thing. 꺼지는 comes from 꺼지다, 'to go off, to switch off by itself'. It is used for lights, fires and devices: 불이 꺼졌다 (the lights went out). A phone that 꺼지다 has died or shut down on its own, which is exactly the kind of accident this grammar loves.

Now the pattern. 바람 is the word for 'wind', and 바람에 is 'in the wind of'. Picture a gust blowing you off your path. That image is the whole meaning: some sudden event pushed things in a direction you did not choose. Attach -는 바람에 to a verb stem and keep it in the present form even though the event is over: 꺼지는 바람에, not 꺼졌는 바람에. The past tense goes at the end of the sentence instead.

네 전화를 is 'your call': 네 (your), 전화 (phone call) and the object marker 를. 못 받았어 is 못, 'couldn't', plus 받다, 'to receive', in the casual past. 전화를 받다 is the standard expression for answering the phone. Notice the shape of the whole sentence: unexpected cause, then a bad result in the past. That is the rule. You cannot follow -는 바람에 with a command or a plan, and it sounds odd with good outcomes.

Compare it with -아/어서. 휴대폰이 꺼져서 못 받았어 is a plain reason. 꺼지는 바람에 adds a sigh: it was beyond my control. Swap the cause and you have an excuse for every occasion: 배터리가 나가는 바람에 (my battery ran out), 갑자기 잠드는 바람에 (I suddenly fell asleep), 회의가 길어지는 바람에 (the meeting ran long). Whether the other character believes you is, of course, another episode.