Ethernet Magnetic coil ground
Ethernet Magnetics are used for providing the isolation between the interface. The reason behind that is the safety and the different potential of linked system. Since the system can be on different ground level so we donot connect the primary and secondary side with the same ground.

The other reason behind that is if the cable gets short with a high voltage, PCB will be saved from getting damaged.

So basically the reason for providing the two separate ground is to isolate the two system.

If we connect the both end with the same GND as shown below, the system will not be isolated.



If we want to provide the isolation between the two system we should connect the system as shown below.