This is a video by Gerbert Kuiper demonstrating what happens when an ArduPilot hexacopter loses a motor and a description of the relevant parts of the motor driver as well.
This vehicle responds quite well because it has a good power to weight ratio. For vehicles with less power reserve the response is similar but the vehicle will also lose altitude. As a side note, there is more that we can do to improve the hexacopter’s response and it is detailed by our control expert, Leonard Hall, here.