Question

"Our dog LuLu had broken her leash, and rounding the corner of the house, the shrub caught her in the eye." This statement:

includes an inappropriate combination of modifier and noun.

*** includes a passive construction-one in which the subject receives the action of the predicate rather than producing the action.

includes run-on independent clauses.

includes a shift in person

is a sentence fragment.

Answer 1

There is no passive in here.

Lulu did the breaking of the leash. (active)
The shrub did the catching ... (active)

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It's also not a run-on because of "and" in there.

It's not a fragment.

I don't see any shift in person either; all nouns and pronouns are in 3rd person (no "I" or "you" in the sentence).

The only one left is the first answer choice, but I don't know how your text has defined "inappropriate combination of modifier and noun."