Consider an overhead transmission line (not cable) and from whatever reason, one phase is out. Now, if secondary side of transformer at the beginning of transmission line is grounded star, there will be some not negligible voltage in the phase that is out (potential difference between line and ground). On the other hand, if secondary side of transformer is delta, voltage of phase that is out will be zero. Why is that happening? Type of load doesn't matter, it is not affecting this results. These are voltmeters connected to ground
The delta transformer is galvanically isolated from ground. If both connected phases are neither connected to ground (e.g. via incorrect installation or defective device etc.), there is no potential difference between the disconnected phase and ground - even with the phase connected, there is no potential difference - in other words, the ground is not involved at all in this circuit, unless there are no other unshown elements with connections to ground.
In the other case with the grounded star, any unshown device that is connected to one of the 2 or both uninterrupted phases and the interrupted phase could produce dangerous voltages at the "disconnected" phase.
That is why e.g. in Europe the power transmission lines are switched off alltogether (all 3 phases), even if there is a problem with 1 phase only , i.e short, undervoltage, load limit etc.