When a solid signal is applied to the base of an NPN transistor, it allows collector current to flow, effectively saturating the transistor and enabling it to act as a switch. This saturation results in a low voltage between the emitter and collector, allowing current to flow through the relay, which activates it. The relay turning on indicates that current is indeed flowing through the transistor, which generates a magnetic field necessary for the relay's operation. If a faulty transistor short-circuits the collector and emitter, the relay may still activate, but it would remain on without base current. Understanding the relationship between base current and collector current, influenced by the transistor's gain (hFE), is crucial for circuit functionality.