How Does an Unearthed Socket Close its Circuit?
You are confusing the point of the earth ground wire.
In all situations the current is supposed to flow between the phase and the neutral. The ground is just there to offer an alternative path back when a problem occurs with the live wire.
The power is generated across three phases, but that doesn't matter all that much, then at some point the neutral is connected to earth, like this:



simulate this circuit &ndash; Schematic created using CircuitLab
Now, the Earth is safe, we are all connected to it, so, nothing weird happens when we touch it. But if a device is grounded to it, and internally a phase wire comes loose and connects to a metal case, such as in a washing machine, then the current has a safe path back to neutral through the earth.
The one exception to my drawing is a single-wire system, where the Neutral is skipped in sub-station to house distribution, but that is excessively rare these days, but that would look like:



simulate this circuit
But here your house itself still has a phase, a neutral and a power earth. In some countries the neutral wire is there, but they connect to earth at the house as well, but still there will be a phase, a neutral and a ground inside the house. And a well functioning device will never conduct to ground (with the exception of earthed appliances in wet locations, such as washing machine in the bathroom - they are usually allowed to leak to ground).
Many modern systems in-house have an Earth leakage detection that trips when more than a certain current (between 5mA and 50mA usually, depending on local regulations) disappears between phase and neutral. That would mean if everything conducted to earth by default your earth leakage detector will keep tripping. This leakage detector is there to cut off the phase voltage in the case that you decide to lick a phase wire and such conduct current back to earth. That current doesn't come back through neutral, so the protector trips and saves your life.
Edit (update):
The leakage detection is connected like this, to clarify:



simulate this circuit
The current in AM1 and AM2 is compared, if there is a difference larger than a set value the switch opens. So in whatever the situation, if there is current going to earth, through the wire or through you, the switch will open.