This is the LibrePilot forum. I would guess that questions about Pixhawk would be better answered on a PixHawk forum.
The following are my considered beliefs after some study a while back. I am certainly open to discussion about them if someone wants to discuss.
It depends a lot on how many motors your multicopter has and how powerful they are. Assuming some things, like the bad motor isn't draining the battery horribly, an octocopter pretty much automatically supports motor failure as it is basically two quadcopters bolted together and if one of these quadcopters alone can lift and fly the load, you can see that it will work. A hexacopter can support motor failure but will not be able to yaw in one direction and will get some undesired yaw during roll and pitch commands but can remain flyable if flown smoothly and gently and knowing that you may need to yaw left 270 instead of right 90. I would guess that octos and hexas are pretty much normally, automatically support by most firmwares, assuming the PIDs (et al.) are well tuned.
Ted talks shows that even a quadcopter can support motor failure, but the quad spins (yaw) fast and continuously and though it can fly in a straight line, the pilot has a hard time knowing what direction that will be until he tells the quad to move forward and see what direction it flies. I'm not aware of any normal drone firmwares that support this, and there is some hardware that can't even support it if the rate of spin is too fast for the gyro's hardware spin speed limit or if the vibrations are too bad for the hardware vibration limit.
And of course there are some failures where it is just not practical to have a fall back. What if an ESC shorts out and drains the battery? What if the FC fails? What if the GPS fails? I can't think of any motor failures I have had "in the air", they have generally been from crashes or getting blades caught in the grass, or similar. OK, maybe one from a factory bad solder joint that separated.
I feel it's better to build two quads from mid grade parts than one octocopter which still might fail for other reasons even when built with redundancy from expensive parts. IMO the only time where it might pay to build an expensive octo or more is if you are flying a VERY expensive camera (or your own butt
).