To understand what, exactly, is dangling here, it’s worth pausing for a short refresher.
Danglers, which include dangling participles, are typified in sentences like “Walking down the beach, my shoulders got sunburned.” Clearly, the writer didn’t mean to suggest that his shoulders were walking. But the way he structured his sentence inadvertently said just exactly that.
The participial phrase “walking down the beach” is supposed to modify a noun — the person doing the walking. We would indicate this by placing the noun or pronoun being modified immediately after the modifying phrase: “Walking down the beach, I got a sunburn on my shoulders.” Because “I” comes right after the “walking” phrase, there’s no doubt it was the thing being modified.
But when you put something else after the modifying phrase, suddenly you’re saying something you never meant: “Walking down the beach, my shoulders…” doesn’t work because readers have come to expect that the thing being modified will come right after the comma.
Verb participles like “walking” aren’t the only things that can dangle. Even nouns and noun phrases can. “A man of great courage, Jane watched the soldier march by.” This sentence is structured in such a way as to suggest that Jane is the man of great courage, when in fact the writer (probably) meant the soldier.