Sorry to hear that

, ive had this happen a number of times and i guess the overhead water gets trapped in the new growth and slowly rots it away. My rookie advise would be if the bottom area of the new growth near the media is mushy or rotten i would take a sterile razor and cut it off as near to the old pbulb as possible and get as much mush as possible out of there so it wont spread.
Now if the pbulb is still solid and a nice green color i'd probably just remove the leaves that come off easily and wait a few days and see what happens. If it spreads cut that growth off and sprinkle with cinnoman. If not then it should continue to grow fine.
Good luck and i hope that it pulls through!
Ben