When she sang she could make a fence post cry.
I received this answer from a reliable source that the whole thing’s a metaphor, last part is anthropomorphizing (the fence crying).
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There are a few rhetorical devices going on.
The last part is indeed a kind of personification, or attributing a human quality (crying) to a nonhuman entity. This serves a larger metaphor: a fence post, which theoretically can't cry, nonetheless being moved to tears is the vehicle for conveying how moving her singing is (the tenor). With her singing, she could move even someone who usually does not express emotion. Another way to describe how this metaphor works is hyperbole: an immovable object being emotionally moved is an exaggeration compared to a stoic person being moved.
Why is a pathetic fallacy not involved? Traditionally, a pathetic fallacy refers to natural objects or phenomena: clouds, lightning, leaves, and rocks. A fence post is not natural. It also emphasizes how the perspective of a poet or artist is impressed upon these objects. I find that difficult to argue for in your example.