A. When the truck is turned off, the charge to the battery stops. Any load attached and turned on will drain the battery. One way to prevent over-discharge is to turn some loads off, especially larger loads. Another way is to set LVDs (Low Voltage Disconnects), on devices that have this option, to a higher voltage.
This is why Xantrex inverters offer multiple LVD settings. For example, setting the inverter LVD to a higher level (like 12.1V), the inverter will turn off before the battery is significantly discharged, and the truck will have an easier time starting in the morning. But if your inverter LVD is inadvertently set for 10.5V, the inverter will continue to drain the battery until it reaches a level too low to be able to start the engine in the morning.