When the base current in a Bipolar Junction Transistor (BJT) is zero, the transistor enters cutoff mode, meaning it does not conduct current between the collector and emitter. In this state, there are no charge carriers injected into the base region, leading to a lack of electron flow from the emitter to the collector. As a result, the collector current also drops to zero because the transistor cannot amplify any input signal without base current. This behavior is crucial for understanding how BJTs operate in switching applications. The discussion emphasizes the importance of base current for transistor functionality.