Current on human with grounded electrical device
There are two scenarios. The resistance of the phase is low or the resistance of the phase is high.
If the resistance of the phase is low, a ground connection will trip the protection device. Protection devices with a dead short are typically very fast.
In the case that the phase has enough resistance that the protection device does not trip things get a bit more complicated. Suppose the feed is 120V and the protection device is 15A. The resistance of the feed will need to be at minimum 8ohms to keep the protection device from tripping. A good ground resistance will be sub 1ohm. We can calculate the voltage drop using those numbers. 120*(1/(8+1)) = 13V. About 13V would appear on the case worst-case scenario.
Finally the human touching the case. The resistance of the human body varies but 1500ohms is a good worst-case scenario. If we put 1500ohms in parallel with 1ohm the current divider gives us about 10mA. That is considered a bad shock but not lethal. This is far reduced when the resistance of the ground is lower.
Something that I want to note; is that the case of the phase having enough resistance not trip the protection is highly unlikely. At the very least it would not go unnoticed for any extended period of time. There would be 1800 watts of power being dissipated and that would most likely catch something on fire.