Thank you for waiting. I had hoped to find out what happened with the leaves because it can be normal for this species to lose its leaves in the winter. However, if that were the case, there should be new growth by now. It is also not normal for the stem to droop, and that is often a sign the plant si dead. If you find green, living plant tissue after scraping off the bark, there may be hope. In that case, cut off the trunk and wait to see of new growth sprouts from the stump. I suspect you won't find green tissue, and that means the plant is dead. The species is not really a palm, but is a succulent, requiring little water. The most common cause of problems for it is over watering. That will cause the roots to rot, followed by leaves dying, and the trunk/stem going limp.
The Madagascar palm needs a well-drained soil, and should only be watered when the top several inches are dry. In the winter, it needs even less. Many horticulturists recommend no water at all in the winter. It also requires full sun to stay healthy, so your site with afternoon shade is not ideal. As for feeding, a good all-purpose liquid fertilizer should be applied at half-strength in the spring. Dilute it with water to get half-strength. No fertilizer should be used in the winter. Here's a website where you can confirm this information:http://www.gardenguides.com/95743-care-madagascar-palm.html
I suspect that your tree began normal leaf shedding in the fall, and in hopes of saving it, the caretaker watered it. Since the plant doesn't need much water in the winter, it probably developed root rot.
If you have more questions, let me know by clicking on REPLY. I'm sorry that you lost a beautiful plant, and I wish you success with the next one.