How was the grounding system working when a ground fault appear, and where the fault current flow?:)

Is this what your asking?

The 120V GFCI looks for an imbalance (~5 mA) in the HOT and Neutral legs.

Since G and N are connected together, we have a path to earth and it's a non-isolated system.

Suppose you had a metal cased 2-conductor corded drill (they don't make them anymore) and were drilling something standing in a puddle of water. The case becomes live because of a defect. Your body touches the drill and you happen to be standing in a puddle of water outside. A small amount of current will be diverted through your body, activating the GFCI and it turns the source off. DON'T TRY THIS AT HOME.