What if we plug in a cable into a socket & then connect both live & neutral wire with a conductor?

short circuit, fire .tripping of overload if provided.

Electricity , like most things, takes the path of least resistance. So if the live line had a choice between going thru the conductor or thru the neutral, the majority of the current would run thru the lesser resistance of the neutral and therefore short circuit.

Following Kirchhoff law, the current will divide between the neutral and the conductor and the current will go in proportion to the resistance difference between the two. But since a neutral has almost negligible resistance, the biggest majority will follow into the conductor since the resistance will be higher either caused by a filament of coils or resistors or whatever is in the conductors circuit.