Signs of a possible cockroach infestation include:

The presence of unusual smells can indicate a cockroach infestation because these pests often produce a distinctive, musty odor. This smell comes from the oils they secrete as well as the waste they leave behind, which can linger in areas where they nest and travel. The odor is often one of the first signs that property owners might notice, prompting them to investigate further for other signs of infestation.

When considering the other indicators of cockroaches, while damaged packaging may suggest some pest activity, it is not exclusive to cockroaches and can involve various other rodents or insects. Similarly, gnawing or scratching noises typically relate to pests like rodents rather than cockroaches, which do not make significant noise. Lastly, finding fur is common with rodent infestations, as cockroaches do not have fur. Thus, unusual smells are a more direct and identifying characteristic associated with cockroach infestations, making it the correct choice in this context.