Delivery drones used by logistics companies today are equipped with unshielded propellers, which represent a major hurdle for in-hand parcel delivery. The exposed propeller blades are hazardous to unsuspecting bystanders, pets, and untrained users. One solution to provide safety is to enclose a drone with an all-encompassing protective cage. However, the structures of existing cage designs have low density in order to minimize obstruction of propeller airflow, so as to not decrease efficiency. The relatively large openings in the cage do not protect hands and fingers from fast rotating propellers. Here we describe a novel approach to safety and aerodynamic efficiency by means of a highdensity cage and morphing arms loosely inspired by the box turtle. The drone cage is made of a dense and lightweight grid. When flying in proximity of humans, the arms and propellers are retracted and fully sealed within the cage, thus making the drone safe and also reducing the total footprint. When flying at cruising altitude far from people and objects, the arms and propellers extend out of the protective grid, thus increasing aerodynamic efficiency by more than 20%.