Depending on the application there are different layers of safety surrounding these systems, including perimeter guards, optical barriers, limit switches, resistance based detection and so on. But when a system is broken someone has to go in and fix it, and you tend to do that with the robot powered up, some of the safety systems disabled so you can actually work on it and if you're really unlucky a motor will end up shorted against a + or - rail while you're within reach. This is obviously dangerous, and it is more dangerous because broken equipment can't be trusted to behave in a predictable way.
They won't stop. Not until whatever is obstructing has moved or the motor has burned out (or someone has the presence of mind to hit the e-stop). I've seen a 3" thick mount that must have weighed well over a ton sheared clear of its bolts (which themselves were an inch thick) by a malfunctioning servo on a very large lathe under construction (think 8 foot chuck for crane cable idler wheels). Do not fuck with servo systems unless you are 100% sure they are safe to approach or you may well end up dead or gravely injured.
My own process to ensure things were safe was to first run it in air without the spindle powered up, then on foam, chalk, and finally on aluminum in that order before progressing to steel.
And that saved my ass more than once.