Trim away the rot. The old backbulbs rarely grow new roots on the Cats. Phals will gow new roots when they get around to it. Repot into new medium that has been soaked in KLN solution mixed as per the label for transplanting. Dry off the old roots (whatever remains.) Sprinkle some generic cinnamon on the cut ends of the roots (or use a q-tip). Let sit overnight to be sure they are dry. Place in pots with new mix that has been treated with KLn and hold down with wire clips designed for this process such as
Kelley's Korner Orchid Supplies Rhizome clips. I've made my own from twist tie material on occasion. The idea is to hold the plant so it won't move in the pot. If there are any viable roots at all, then they may take over and even grow side roots (Phals sometimes do this). But with Cats you are waiting for the new growths to mature to the point where new roots appear. If there are no viable roots at all, then I would place the repotted plant in a plastic bag to hold some humidity. Watch for mold growth, though. Others probably will have some better advice.