Said the story in the Ottawa Citizen:
The woman was trapped in her car unconscious for about 20 minutes while firefighters performed an extraction, he said.
And alert Language Log reader Diane commented: "I had no idea our firefighters were also trained at dentistry!" She also asked me whether the misleading phrase an extraction was a dangler (an analog of the dangling modifier that prescriptivists warn against).
It isn't, despite the fact that we are not directly given a logical subject for the implicit reference to extracting. An extraction is a noun phrase (NP) functioning as direct object of the verb performed, and a direct object never needs a predicand (or "logical subject", i.e., an NP it can act as a predicate of). It's only predicative adjuncts that can be danglers.
It is possible, though, for a predicative adjunct to consist of nothing but an NP. That occurs in A skilled fireman, Dan didn't take long to get the woman out of the vehicle, where Dan is the predicand so we understand that Dan is being described as a skilled fireman. But such an NP can also be a dangler, as in ??A skilled fireman, things didn't take long, which sounds deeply weird because you aren't told who is a skilled fireman.
Diane is of course quite right that the sentence in the Citizen sounds extremely silly. I actually think it's a case of nerdview: perform an extraction must be how fire station record books and regulation manuals would refer to getting trapped women out of crushed vehicles. A reporter with sense would have translated the nerviewese and said "The woman was trapped in her car unconscious for about 20 minutes while firefighters got her out."