As I understand it, the standard use of a participle phrase is something like,

The man walked into the room smoking a cigarette.

In this case, the subject for the participle phrase smoking a cigarette is given by the preceding clause as man. But it's common to see people write sentences like,

The man walked into the room, smoke coming from his cigarette.

In this case, the participle has cigarette for its subject. And that's weird because, in this sentence, "cigarette" has no verb. It's just a noun being modified by this participle. So the form of the sentence

The man walked into the room, smoke coming from his cigarette

is equivalent, I think, to

The man walked into the room, cigarette.

On its face this is totally ungrammatical.

However this latter kind of sentence is very common, and often it doesn't sound too bad. It's definitely a clunk-prone sentence form — especially when the participle phrase is really disconnected from the preceding clause, as in

The man walked into the room, snow gathering on the windows

— but it often works well.

I don't have much technical knowledge of grammar so this is past the frontier of my understanding. I'm really curious to hear a take on this sentence form from someone who's more knowledgeable than me.