The system is designed to be safe, and turn off all power to the car either when the charger demands it (the charger being a part of the car) or if the connector is unplugged. The only exception to this is if someone decides to do something a bit unsafe, such as use a non-interlocked commando outlet to charge using the UMC, or similar portable EVSE unit and then pulls the commando connector out when charging. Definitely not at all sensible or safe..
The way the system works may be of interest. All that's inside a charge point, or the UMC (I'll just use charge point from now on), as far as controlling charge is concerned, is a circuit that energises a low voltage (+12V to -12V) control pilot line, this is the small pin to the top left looking at the connector on the car. There is also a proximity signalling pin, the one that seems to be inset slightly.
Initially, the charge point applies +12V DC to that connection, fed with a source impedance of 1,000 ohms. In this state, the contactor in the charge point, that switches mains power on and off to the car charger, is open, so the power is off. As soon as the connector is plugged into the car, a resistor to ground inside the car charger loads the +12V DC down to +9V. The charge point detects this voltage drop and switches on a 1,000 Hz pulse train on the control pilot, with the voltage ranging from the loaded +9V to -12 V.
The duty cycle of this pulse train (the ratio of high to low time) tells the car charger the maximum current that is available from the supply. The charger then sets itself internally to never draw more than that maximum current, and when it's done that it switches an additional resistor on to the control pilot to load the positive going side down to +6V.
The charge point senses this additional voltage drop and turns on the contactor to supply mains power to the car. The connector on the car is normally latched in place by a locking pin that is driven by a small motor into the slot visible at the top front edge. This holds the connector in place until commanded to release. The command to release the latch is always after the car has signalled the charge point to turn off, by disconnecting the second load resistor. If the latch failed, and the connector was pulled out, because the proximity pilot pin is deliberately made shorter it always disconnects first. The instant it disconnects it signals the charger to switch off and stop drawing power, to prevent any arc. The charge point will then turn off power to the cable as the control pilot will no longer be loaded, making the cable safe.
There are other safety measures included to detect things like the cable being damaged, chucked in a bucket of water, etc, to ensure that the cable cannot be energised when not plugged in to the car.