"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.

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."

The correct answer is: includes a shift in person.

To identify if a sentence includes a shift in person, we need to examine the subject of the sentence closely. In this particular statement, the subject starts with "Our dog LuLu," which is in the possessive form of the first-person plural pronoun "our." However, the verb phrase that follows, "had broken her leash," shifts to the third-person singular pronoun "her." This shift from first-person plural to third-person singular indicates a shift in person, which is grammatically incorrect in this sentence.