Remember that in all cases (currently), the communication between the FC and the ESCs (and therefore the motors) is strictly
one way, that is to say: the FC is
never aware of whether its commands to the ESCs are being obeyed or not, and
never aware of a motor stopping, a prop breaking, or whatever. In technical terms, that side of it is "open loop", i.e. there is no feedback - there is no path/mechanism for such feedback. Furthermore there is no code that says "if one motor stops then speed up this motor or slow down that one - such code, if it existed, would be called "adaptive", i.e. able to adapt to new/changed/different circumstances.
However, the other side of an FC - the gyros, accels, etc. -
IS closed loop - i.e. the code is
constantly trying to bring AttitudeActual and AttitudeDesired together by the only means available to it: varying the throttle setting of each of the motors. So whether or not it continues to fly with a motor/prop out depends
entirely on the number of surviving motors involved, their positions and their relative contributions to the lift/control (as determined by the mixing table). It's therefore not even possible to generalise and say that
all 8-motor MRs
will survive the loss of a motor/prop. Too much will depend on the precise mixing set-up, the algorithm controlling the flight stabilisation, the attitude/inertia of the craft at the moment of failure, the reaction/input of the pilot, the CG balance of the craft, the prevailing wind, etc... etc... etc.
Nevertheless, many 8-motor craft (and, indeed many 6-motor craft) can and do survive such an event. What one
can say is that the more motors you have, the better the chance of surviving the loss of one of them. Further, this "possible redundancy" starts at 6 motors, i.e. 4 motors will
never survive, but 6-motored layouts tend to be more sensitive to the variables in play at the time (as compared to eight motors).
But... (there's always a "but", isn't there?)... statistically, a "failed motor" is probably the least common crash cause of all. From my observation across all the forums, broken props and self-disconnecting wires (along with poor soldering) are the leading causes (after pilot error, of course), followed closely by battery failure. It's easy enough to guard against the connection-linked failures (if you're aware of the importance). Avoiding cheapo battery packs reduces the risk of that cause. Good props (and a ruthless exchange policy if
any damage/impact is experienced/observed) reduces that risk. Btw, one significant likelihood of a broken prop is that the pieces will take out an adjacent/nearby prop - pretty much negating all the redundancy possibilities.
My own conclusion, attempting to balance all these factors, is that an X8 represents the best layout possible for carrying a big/heavy/expensive camera, not because it has better redundancy than a flat-8 but simply because it's more compact/manageable.
However...

... the next generation of FC/ESC
will have closed-loop feedback. The only one I know of right now is the forthcoming OpenPilot Revolution which, when combined with the (forthcoming) OP-ESC will know if a motor is obeying its commands (and should even be able to deduce that a prop is broken). With such feedback it will be possible to write adaptive code that, whilst not able to change the basic physics of the problem, should greatly increase the likelihood of a safe, controlled landing following a component failure.