Absolute phrase

An absolute phrase is a noun paired with a participle or other modifier — 'his hands still shaking' — that qualifies the entire sentence it attaches to rather than any single word in it.

He signed the form, his hands still shaking. The phrase has a subject of its own, his hands, and a participle, shaking, but no finite verb, so it cannot stand alone. It also does not attach to any one word. It qualifies the whole act of signing.

That independence is what makes it useful, and it is the one phrase type immune to the dangling modifier: because it carries its own subject, there is nothing for it to misattach to.

For fiction it is the most economical way to give a speaker a body.

"It is fine," she said, one eye on the door.

Compare the alternatives. She said it while keeping one eye on the door is clumsier. She said it. She kept one eye on the door. breaks the moment in two. The absolute keeps the line and the body in one motion, which is why it beats an adverb in a dialogue tag nearly every time.

Stacked, absolutes build the classic cumulative sentence: He came up the steps, coat over one arm, hat in the other hand, the rain already behind him.