In what condition will the cabin become pressurized according to the air pressure management system?

The cabin becomes pressurized when the negative pressure relief valve engages because this valve is specifically designed to balance air pressure differences that occur in the cabin during flight. When the aircraft is in flight, external air pressure decreases with altitude. If the cabin were to experience a lower pressure than the outside atmosphere, the negative pressure relief valve activates to allow outside air to flow into the cabin, thus maintaining a stable and pressurized environment.

The other options do not directly trigger pressurization. Closing the doors alone is necessary for maintaining pressure but does not result in pressurization by itself. The engine starting is important for various systems, but it does not initiate cabin pressurization. Initiating descent can lead to decompression rather than pressurization since as the altitude decreases, air pressure generally increases in the cabin without needing to engage the negative pressure relief valve. Thus, the specific action of the negative pressure relief valve is crucial for maintaining cabin pressure under varying conditions, making it the correct choice.