You've heard the expression "follow the money" well it's similar for trailers only it's "follow the power". Power comes in and goes to the main breaker. Is there power there? Is it turned on? Were you checking at an outlet that's GFCI protected and it's tripped?
Pinpoint where the power stops and you'll have your answer.
If the trailer's plugged into shore power there's no harm but also no reason for the inverter to be on. If the trailer's not plugged into shore power, yes, there is a small standby draw and it shouldn't be left on for extended periods.
Ron
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