nominative absolute
Definition - A free-standing part of a sentence that describes or modifies the main subject and verb.
Note: It is usually a participial phrase that begins or ends the sentence.

Example -
In the following the nominative absolutes are bolded:
(1) The roads being icy, we decided to postpone the trip.
(2) Their mullets bouncing, the hockey players ran from the burning biker bar.

Oxford English Dictionary -
The term's first citation is from 1843:
"Other idioms … have the indeterminate pronoun preceded by a nominative absolute."
(Proc. Philol. Soc. 153)

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