As a
commercial electrician I have to giggle a little at the the extreme lack of a basic
electrical theory among most laymen.
Without a reference the
safety ground is doing nothing. it can't. The only path back to the source is the two ungrounded conductors provided. The source is not referenced to ground so either wire (but obviously not both) can harmlessly touch unguarded metal and absolutely nothing will happen.
A floating neutral is used at times as a
safety feature and a "safety ground" does absolutely nothing in these instances. I've installed isolated transformer systems in operating theaters where there was an
equipment ground but it was not connected to the secondary of the source in any way other than only as a very sophisticated
sensor device to measure and ensure there was no leakage from either of the two floating ungrounded conductors being used with the
medical tools on the table. If there was any leakage nothing bad would happen intially -no shocks, no
current flowing to ground, other than an
alarm going off at a set threshold and a meter on the panel moving to show the amount of leakage potential.
The first ground is free, and will only reference the leg that is grounded to earth. The second, and subsequently later ground in the other leg is the dangerous one if it should ever happen. The issue with this system is the monitoring for and of that first fault reference.
This same thing happens with a 3-phase ungrounded
delta system used in some manufacturing systems. The system has no neutral and is not bonded on the secondary of the transformer in any way. If any leg were to short out to ground nothing at all would happen. It is not until there is a second ground fault on another leg that there WILL be a problem.
Again, the issue comes in being able to
monitor for that first fault so it can be found and corrected before the second one ever happens.
Cheap ungrounded inverters do not have this sensing capability. They are totally safe until there is a short in one of the wires. That short will go unnoticed until there is a second short, when fault
current may flow and someone may be injured by energized
parts.
Did you get all that? I didn't think so.