bureul kyeon chaero jamdeureosseoyo.

켠 comes from the verb 켜다, which means to turn on.

In this sentence, 켠 is the verb in its adnominal/modifying form:

• 켜다 → 켠

It describes the state of something as turned on.
So 불을 켠 채로 means something like in the state of having the light turned on.

-ㄴ 채로 means while staying in that state, with something left as it is, or without changing that condition.

So:

• 불을 켠 채로 = with the light left on
• 문을 연 채로 = with the door left open
• 안경을 쓴 채로 = with glasses still on

In this sentence, it shows that the person fell asleep while the light was still on.

Because 불 is the object of 켜다.

• 불을 켜다 = to turn on the light

So inside 불을 켠 채로, the phrase still keeps the object marker 을 because the light is the thing being turned on.

You can think of it as:

• 불을 켠 상태로 잠들었어요
  = They fell asleep in the state of having turned on the light

The noun 상태 is omitted, but the object marking stays.

Because 채로 attaches to the modifying form of the verb, not the usual plain past form.

For action verbs, that modifying form is often -ㄴ / -은:

• 먹다 → 먹은
• 닫다 → 닫은
• 켜다 → 켠

So:

• 불을 켠 채로 is correct
• 불을 켰 채로 is not correct

Even though it may feel like a past idea in English, Korean uses the modifying form here to describe the resulting state.

잠들다 means to fall asleep, while 자다 means to sleep.

So:

• 잠들었어요 = fell asleep
• 잤어요 = slept

That means this sentence focuses on the moment or event of drifting off to sleep, not just the fact that the person slept.

Compare:

• 불을 켠 채로 잠들었어요
  = They fell asleep with the light on.
• 불을 켠 채로 잤어요
  = They slept with the light on.

Both can be natural, but 잠들었어요 is more specific here.

You can, but the nuance is different.

• 불을 켜고 잠들었어요 = turned on the light and fell asleep
• 불을 켠 채로 잠들었어요 = fell asleep with the light still on

The -고 version mainly links two actions in sequence.
The -ㄴ 채로 version emphasizes the unchanged state during the second action.

So if you want to highlight that the light remained on, 켠 채로 is better.

They are very close.

• -ㄴ 채
• -ㄴ 채로

Both can mean in that state.
채로 often sounds a bit more complete or explicit, and it is very common in everyday Korean.

So:

• 불을 켠 채 잠들었어요
• 불을 켠 채로 잠들었어요

Both are possible, but 채로 may sound a little more natural to many learners at first.

잠들었어요 is in the polite informal style, often called 해요체.

Breakdown:

• 잠들다 = dictionary form
• 잠들었어요 = past tense polite form

This is a very common everyday style: polite, natural, and not overly formal.

Other versions:

• 잠들었습니다 = more formal
• 잠들었어 = casual/plain intimate

Often, yes, that is the natural implication in context, but the grammar itself does not force that meaning.

Since people usually do not intend to sleep with the light on, 불을 켠 채로 잠들었어요 often sounds like:

• they forgot to turn it off
• they dozed off unintentionally
• they were too tired and fell asleep

But strictly speaking, the sentence only states the situation: they fell asleep while the light was on.

불 originally means fire, but in everyday Korean it is also very commonly used to mean light or lamp/light source, especially in expressions about turning lights on and off.

For example:

• 불을 켜다 = turn on the light
• 불을 끄다 = turn off the light

So in this sentence, 불 is understood as the light, not literal fire.

Yes. -ㄴ/은 채로 is a very useful pattern.

Examples:

• 문을 연 채로 나갔어요.
  = Left with the door open.
• 신발을 신은 채로 들어왔어요.
  = Came in with shoes still on.
• TV를 켠 채로 잤어요.
  = Slept with the TV on.
• 가방을 든 채로 기다렸어요.
  = Waited while holding the bag.

So the pattern is widely used to describe doing one action while keeping another state unchanged.