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This is intentional. It's not a behaviour that's been explicitly scripted: the idea is that a propeller that is damaged / broken can produce less thrust. This creates an imbalance, and it's the PID controller duty to "deal with it". Although, when the damage is too big, it creates oscillations and the drifting you experienced.
This part makes sense. Let's take roll, you can see it as being produced by a difference in rotation speed between the 2 left propellers and the 2 right propellers. Let's say 1 of your right propellers is broken, the flight controller (PID controller + mixing logic) will have the other right controller spin faster to compensate. (This is a simplified explanation, mixing has to happen on roll, pitch and yaw at the same time, but this explanation gives an idea of how the underlying system operates)
Now, during testing, it seemed that most drones (it gets trickier for low powered ones) can fly with a (very) damaged propeller, although 2 broken propellers is where you start loosing degrees of freedom and essentially cannot fly well.