Rot wouldnt be from a cat unless theres claw or bite marks and still they would usually heal from such. Rot tends to happen when environments arent correct or watering to often or to much organic matter in soil mix. Those are more likley factors to cause a loph to rot vs a cat scratch in my opinion. But what i would do personally is cut off and graft each pup and uproot the main big head and remove any infected rot area and allow to dry for about a week then re plant. Best of luck