Regarding plugging operations
Negative slip simply means that the rotor is rotating faster than the rotating magnetic field.
During plugging the slip is increased to 2-s where s is the original slip so it does not produce negative slip.
Negative slip can occur in other circumstances e.g. if an electric car is running downhill the rotor of the motor can be rotating faster than the magnetic field.
This can be used to allow the motor to brake by regenerating electricity, in order to do this the rotation speed of the magnetic field needs to be controlled and the negative slip kept reasonably small in order to keep power losses within the rotor under control.