Are you talking commercial machines or hobby machines?
For commercial machines this is my experience.
E-stop is not really applicable to overtravel because that is either detected by software limits or in the absence of these by limit switches. Most likely it will be software limits which means that when running a program the machine knows it will overtravel so it doesn't even attempt the move. In handle jog it will brake to a halt as it is jogged to the limit.
In the case of crashes generally E-stop is probably irrelevant because the machine has probably crashed, overloaded the servos and/or spindle and alarmed out long before you can hit E-stop.
However, the alarm condition resulting from a crash is similar to E-stop and recovery can often be as simple as clearing all the alarms and then backing the spindle/table away in handle jog. In some cases it can be a bit more difficult such as when you have friction welded the tool or tool holder to the workpiece or vise. Then you have to get creative.