The net resultant flux being zero does not induce any current in the secondary of the transformer. Thus the secondary current of the core balance current transformerwhen all the three phases are healthy is zero.
When an earth fault occurs in one of the phases, the zero-sequence fault current which flows is not cancelled by the flux of the other two phases and hence induces a current in the secondary.
The core balance current transformer can be connected to an earth fault relay which can be used to generate the tripping signal.