The answer is: It’s complicated…
The easiest solution to this problem is to stop using the inverter before it gets to that point.
At that point, or even before, you will typically experience drivability problems.

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The engine may even die.
This is why leaving the headlights on overnight drains the battery down to nothing.
The same thing happens if you use an inverter when you’re parked.
How Long Can You Run an Inverter Before the Battery Drains?
Bigger loadslike a desktop computer, television, and many other electronicsdrain a battery even more quickly.