dying elements do not overheat, they underheat, and leak electricity into the water until they fail totally. Loose screws might cause an arc and a melt, but again it will not overheat the element itself.
Either you do not repair many heaters or you just replace everything. IF an element burns out NEAR the terminal controlled by the thermostat, it will use the water as a neutral source and heat continuously, although at a diminished rate, which is why it take longer for the high limit to trip and shut off the power. IF the screw/bolt on the high limit control is loose, the added resistance WILL overheat it and cause it to trip, regardless of the water temperature. When this happens the guilty bolt will usually change color.