Well I'm hoping that I am wrong, but it sounds like rot to me. Is it squishy where it is black? If it's rot then she needs to cut it back, soon before it spreads, untill she sees no more of it. I think she should let it callous (sp?) over, and hopefully if she has a good root system going on under the soil maybe it will bust out some more leaves and continue to grow. How often has she been watering it? Possibly too much. You should be getting more reponses here shortly. Good luck with that plummie.
Lauri

When cutting off the black tips you want to go slow and cut a little at a time. Stop once you hit good (white) stem. As Lauri said, the cut should calluse over after a few hours but may take a couple of days. If the rest of the plant is viable with good root system, you should get new branches. After the "surgery" is done, leave in a shady area for a few days then gradually move to full sun.

Also, be sure to sterilize your cutting tool between cuts with alcohol, peroxide, physan, or other disinfectant so you don't transfer the problem to the clean wood or to other plants.
Mike

Thanks so much for the help. She is going to do the surgery this evening.
She's persisted so long with this plant I'd like to see her have success, but it's not looking good right now.