Exceeding the peak inverse voltage (PIV) in a half-wave rectifier can lead to significant issues, including potential damage to the diode and other components like the transformer. The PIV for a single-diode setup is twice the peak input AC voltage. If the diode fails due to excessive voltage, it may short circuit, risking further damage and possibly causing a fire. Conversely, if the diode opens, the output DC voltage will drop to zero, which can occur even without exceeding the specified PIV. Understanding these risks is crucial for ensuring the safe operation of rectifier circuits.