That's just it: The meaning is not clear when a participial phrase or a relative clause is not placed next to the noun it modifies. I think the phrases are misplaced and would rewrite the sentences. Just my opinion.
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Grammar Curmudgeon If it is "a hard and fast rule that a modifier (word
MrPedanticWelcome to English Forums, Reaver!
These seem fine to me: the participle clauses don't dangle, as their subjects match the subjects of the main clauses. And as cakes don't savour, corners don't run, and backpacks don't behave reverentially, there's no chance of confusion.