The electronics/software doesn't really understand or care what configuration your motors are in, or even how many there are. When you set it up, all you're telling it is how to turn left, how to pitch forwards, how to yaw right, etc. That's it. The control system is entirely "dumb" about how it uses that information - it just keeps on measuring the craft's attitude, issuing motor throttle changes to compensate (using the "look-up table" that you gave it when you configured it, then measuring the attitude, recomputing the motor throttle changes, etc. So when a motor fails (for example) the electronics is absolutely unaware that anything has changed. It just keeps on... measuring, computing, commanding, then measuring again. Let's say it's a flat-8 that's lost a motor. Now it has four CW and only 3 CCW engines, so it's going to want to yaw to the right (since the net torque effect will be CW). The electronics will sense the yaw (without knowing or caring what's causing it) and compute that it should increase the throttle on the CCW engines. The correction will happen slower than if there were 4 engines, but it will happen. Similarly, if the wind causes a roll, the correction will happen, just more slowly. Same with pitch. The danger comes when the craft's measured attitude requires simultaneous yaw, roll and pitch correction, all in the direction in which it's "weak" because of the missing engine . There's a chance that the craft will "get away" from the electronics, get so far out of attitude that the electronics decide that drastic full throttle corrections are required. Now you're in the hands of the quad gods: it might settle down, it might flip.
This works exactly the same way with a flat-8 or a coax-8, whether the motor pairs are spinning in the same direction or opposite. It's also the same with a flat-6 or a coax-6, except that because the relative loss of control is greater (1 out of 6 rather than 1 out of 8) it's more likely to get out of control, and quicker. But on a good day it's still possible to get it to the ground in a reasonably dignified way. On a quad the loss of control (1 out of 4) is so great that it will "get away from" the electronics almost immediately.
None of the current systems employ what's called "adaptive" behaviour. They don't know that a motor is stopped or a prop has broken and they have no notion of speeding up healthy engines to compensate for a dead one or switching off engines to restore the net torque effect to zero. To be able to do so they'd need two-way communication with the ESCs, predictive monitoring of engine rpm, etc - none of which is possible with current off-the-shelf RC parts. More advanced projects like OpenPilot will get there sooner or later. MK and the like, I'm not so sure.
Let's not forget also that this "redundancy" covers only a very small percentage of the possible problems that could bring your flight to a sudden end. The MK I2C ESCs, for example - one fails and they'll all shut down - hence the PWM converters that have appeared recently. Batteries can fail catastrophically. The main board can fail. Connectors can come undone. Fatigued aluminium arms can fail in flight. Whatever took one engine out can take a second one out, or take the whole system out. So as an operator you simply cannot rely on this theoretical, "best case" redundancy. Nice to know it's there, but it's no substitute for good components, good maintenance, good piloting, etc. And it certainly should not be the primary reason for choosing a particular number of engines or a particular frame style - with the single exception (perhaps) of NOT choosing 4 engines if crashing is likely to happen with an expensive camera onboard or anywhere near people).
Phew! Lecture over! ;-)
