While the divorced hydraulic system was supposed to allow the front to work if the rear has a leak (or vice-versa) I've found that if one end fails, the other is terribly inadequate at stopping a car.
Technically, it is not an "emergency" brake. It is a parking brake meant to hold the car still after it has been stopped. For that purpose, they work as intended. In an "emergency", they are not as effective as your regular rear brakes since they only engage the rear brake shoe, not both front and rear shoes.
The fix here?
Replace the master cylinder with the appropriate unit.