Answer: Dracaena fragrans "Massangeana" or Corn Plant Dracaena is a very popular houseplant because it is easy to care for and has virtually no problems. At 12 years of age your plant may be reaching the end of its lifespan (living things don't last forever!) I suspect this because its general health seems to be failing yet it is sending out a new shoot. Only time will tell. If the original plant continues to decline, I'd remove the new shoot, pot it up, and discard the original plant.
In its natural habitat it can reach 20' in height; in a container the height will be determined by the container size. Restricting root growth will keep it small. You didn't mention whether or not you've repotted it recently. I hope the soil has be rejuvenated on a regular basis. If not, now might be a good time to repot it in fresh potting soil.
As for the shoot, you can leave it alone and repot your plant into a larger container, or you can gently remove it (roots and all) and pot it up on its own.
You also have the option of cutting off the top of your corn plant and rooting it in sand. You'll have a new corn plant, plus the cut stem on the original plant will send out a new shoot, eventually making a new plant.
Best wishes with your corn plant!
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