While driving your car ,brakes play a major role in handling. If brake force is not properly distributed to front and rear tires then their will be the loss of directional stability or loss of directional control i.e you will not be able to steer the vehicle.
Locking of tire means that force applied by the brakes which is Fb is greater then the force generated between tire and ground contact patch.
Note:- Road camber,road issues,cross winds or because of any other reason your are not able to drive the car straight,continuously you have to steer the vehicle a bit to make it straight. This lead to generation of lateral force.
Lateral force is the support force generated on tire to support the centrifugal force i.e generated at time of steering or turning.
Case 1 :- Rear wheels lock first !
When the car was going straight ,due to road camber,wind etc it has the tendency to shift towards left or right. In this case i am considering that car shifts towards left direction, Now to support the car and prevent it from going leftwards ,tire produce lateral forces. As in this case rear tires are locked ,so they are not able to produce lateral force . But as front tires are not locked they will produce lateral force and will support centrifugal force. Lateral force shown by red arrow on front tires. This force will create a torque about Yaw point or COG of vehicle.
Let's again see this case ,but in different manner:-
In the above figure, you can see that on applying the brakes and locking the rear wheels, will lead the car to rotate slightly as shown in 2nd diagram. Now as rear wheels are locked , so they are not left with any braking force, but front tires are left with the braking force shown by Fbf in 3rd diagram. Now this Fbf will produce a clockwise moment about the COG and will turn the vehicle front to back shown in 4th diagram . Yes ,it is very dangerous as it will yaw your car while braking and directional stability is Lost.
Case 2:- Front wheels lock first !
When the car was going straight ,due to road camber,wind etc it has the tendency to shift towards left or right. In this case i am considering that car shifts towards left direction, Now to support the car and prevent it from going leftwards ,tire produce lateral forces. As in this case front tires are locked ,so they are not able to produce lateral force . But as rear tires are not locked they will produce lateral force and will support centrifugal force. Lateral force shown by red arrow on rear tires. This force will create a torque about Yaw point or COG of vehicle but it will not rotate vehicle completely and will work in different manner.
Let's again see this case ,but in different manner:-
In the above figure, you can see that ,on applying the brakes and locking the front wheels, will lead the car to rotate slightly as shown in 2nd diagram. Now as front wheels are locked , so they are not left with any braking force ,but rear tires are left with the braking force shown by Fbr in 3rd diagram. Now this Fbr will produce a clockwise moment about the COG and will rotate the vehicle again to straight position, shown in 4th diagram . Yes ,it will produce a self returning torque on the vehicle. But locking of front wheels is also not safe as it will lead to steering control loss, as front tires are skidding so you will not be able to steer the vehicle.But this can be corrected by driver.