Well the wire will be thick enough so the original expected amperage will not melt the wire insulation. But the voltage drop will be excessive.
Litigation perhaps. If the fuse for the circuit was too big for the wire.
An inverter was never intended to be plugged into a distant 12v power port. A small inverter powering a light load might not have issues. But the ciggy plug and receptacle will increase their resistance with more use.
If the 12v ciggy receptacle is on the battery with 4 awg wire. The ciggy plug itself would still melt above 120 continuous watts.