You can run bias slicks on the back with radials in the front, my friends car was like that and i know many people that run that on occasion.
The problem is bias ply tires and radial tires dont behave the same way, so mixing them can make things interesting.
Im not completely sure but radial tires can give more and they are more forgiving then bias ply tires when it comes to traction. The rear of the car is what gives the car stability during pretty much any driving condition especially turning.
If the front of the car has tires that get more traction then the rear the car will go into a tailspin, pretty much like pulling the parking brake in a turn. Bias ply tires on the rear of a car, if lost traction during a turn i could see being a big problem. Especially if your not expecting it.