Answer: The fragment that could become a complete sentence by adding only a predicate is "One of the world's most destructive storms".
Step-by-step explanation: A predicate is the part of the sentence that includes a verb or verb phrase, which indicates what the subject is, is doing or is feeling, and, in some cases, modifiers. "One of the world's most destructive storms" could function as subject of a sentence; therefore, it could become a complete sentence by adding only a predicate, such as "was Hurricane Katrina". In contrast, "more than a week after the storm" and "being more universal" need a subject and a predicate and "was the deadliest storm of all time" needs only a subject.