Most inverters will sound a warning when they have drained a battery to near critcal levels. If the vehicle is in reasonable condition it will still start and the battery can be recharged safely.
Sorry this info came so late Nita!
That's a relatively recent development - I have an older (late 80s, early 90s) inverter that was permanently mounted in my Jeep by a prior owner. It does not have such an alarm (unfortunately).