Plantlover, do you know the Dracaenas species? Can you post a pic?
You said, 'I figured this was due to lack of water.' Plantlover, you cannot figure/assume. The thing to do is test the soil. Whether you use a water guage, insert your finger in the soil, or lift pot to check weight. Never assume.

What size is its pot? Pot size, roots, light, soil type, room temp, etc, makes a difference when water is needed. It sounds like your Dracaena was overwatered.
Is the narrowing section in the trunk, soft? Give it a squeeze, check to see if it's mushy. Toni

If there's a brown spot on the stem, and it's a Dracaena marginata, it's probably rotting. See if you can find anything above the spot where the cane is still solid; you might be able to take a cutting from a healthy part of the plant and salvage something.

I am not sure of species, the narrowing of the stem is hard. I have tried uploading some pictures to show you the damage.

Here is a link that might be useful: {{gwi:72462}}

Here is another picture

Here is a link that might be useful: {{gwi:72463}}

Hi Plantlover. Your plant is Dracaena Janet Craig.
Is the brown patch a hole/hollow or firm?
It's hard to tell, Plant.
Let me know if it's hollow, please. Toni

The brown patch is firm.

Is the firmness of the brown patch a good sign that the plant will bounce back? Or is this the beginning of the end?

Here is a link that might be useful: {{gwi:72464}}

That's a Dracaena fragrans or Corn Plant.

Yes that is a bad spot. Dip or spray your pruners with rubbing alcohol. Then cut the stalk a couple of inched below the rot. If the inner growth is whitish green with no brown streaks, the stalk is ok and will rejuvinate a new stalk.

Grip the bark on the main trunk. and feel it. Is is tight, loose or both?

Tight is great both is ok and loose means it's a goner.

As to that top you cut off, spray those pruners again and cut above the brown spot. If the inner cambria is healthy, you can stick the cutting in some fresh dirt and start anew with it.

Either way, good luck!

Firm is good. Though narrow and brown is still weird: I can't come up with a good guess, even.

It's hard to tell if the wilting is caused form lack of water or a result of the plant bing sick. One thing I have realized w/mine is it grows more in the winter months than in the spring/summer. I have to really cut back on the watering in the spring/summer, mine tells me when I water it too much, the bottom leaves turn yellow and eventually fall off. At one time there were three stalks on mine, I lost one to what sounds like you are experiancing. But the two remaining stalks are doing fine. However the stalks are narrow in some place, I do have to stake it to keep it up right.This was taken some time ago, it is now 4' tall.

{{gwi:72466}}