Heard in a tv commercial for life insurance:
There’s no medical exam required. And by answering a few simple questions, your coverage can start immediately.
The boldfaced material has a classic “dangling modifier”, a non-default SPAR: by answering a few questions is a subjectless predicational adjunct to the main clause, and its interpretation requires that a referent be found for the missing subject, but that referent is not the default one, the referent of the subject (your coverage) in the main clause; instead it’s the referent of the possessive determiner (your) within this subject. Despite this, the sentence is easily understood (as something like ‘if/when you answer a few simple questions, your coverage will start immediately’); it may count as a “dangler”, but it’s harmless.
In my collection of many hundreds of danglers, there are only a few like this one (with a coding that begins SUB(by)-PRP), but there is a set of somewhat similar cases that I’ve looked at under the heading of “by-Topicalization”.