Which safety device prevents an elevator from falling if the hoisting cable breaks?

The safety brake is the critical device that prevents an elevator from falling in the event of a hoisting cable failure. This device is designed to engage automatically if the hoisting cables lose tension, effectively gripping the guide rails to halt the elevator's descent. This mechanism provides a crucial safety measure, ensuring that passengers are protected even if a significant failure occurs in the system.

In the context of elevator safety, other devices serve different functions. An emergency stop switch is primarily intended for user-activated operations to halt the elevator in case of an emergency, but it does not act to prevent free fall due to cable failure. A door interlock ensures that the elevator doors cannot open while the elevator is in motion or while it is not aligned with the landing, but it does not contribute to preventing falls. Similarly, an overload sensor detects when the elevator is carrying too much weight and can prevent operation or alert maintenance personnel, but it does not function to stop a fall caused by broken cables. Thus, the safety brake is the essential mechanism that directly addresses the danger of an uncontrolled descent, making it the correct answer.