Alzheimer's sleeping 16 hours a day and not eating much.

Sounds like it's time to bring hospice on board if you haven't already. Sleeping a lot can signal that the end is nearing, but keep in mind that can still mean many more months.
My late husband who died with vascular dementia, slept 16 hours for the last year of his life, and then began sleeping closer to 20+ hours as his end of life neared.

Sleeping more is common in the later stages as is the loss of desire to eat, but don't assume that means the end is imminent because my mom spent years that way. What we can do is offer foods they can eat (often pureed solids and thickened liquids are necessary) as often and as much as they desire, but never force feed. There are many calorie dense supplements available, and remember end of life is not the time to worry about balanced diets, give them whatever they'd like.

It sounds as though you are in the late stages? I know you will have discussed this with the doctor, and that you will understand that this is the norm. And in final stages there is almost a complete loss of swallow, ability to process food, and being bedridden with the limbs contracturing up to a fetal position.

What discussions are you having with doc now about palliative or Hospice supportive comfort care. I am so sorry. This is so difficult to stand helpless witness to.