I don't think the Bible speaks on this either way--therefore, we must make our own judgments. I don't think any of us have the right to speak for someone who has free will and faculties in that situation. Therefore I agree with Chaim, DWI, Skippy, Dr. Dan., etc. on this issue.
At my church, an elderly couple I know went through exactly this. The elderly husband had serious heart surgery about three or four years ago and never really recovered, and simply became an increasing burden on his (able-bodied) elderly wife, as his health went on an exponential downward spiral. Whether it was due to poor lifestyle habits in his youth (which age-related diseases usually are partially attributable to) or simply the irreversible and unavoidable effects of aging, this man became nothing but a burden and life-sapper for his wife, and was completely unable to accomplish any more good or usefulness for his remaining time on earth.
When he finally passed last fall, his wife, though grieving, was relieved, and I can see why.
Now--I would never go around saying who must die, but if this man on his own decided that this miserable existence (which I would call worse than death) was only dragging all of his loved ones down and wanted out, I certainly would not call it sin.
I definitely hope something takes me long before I become a vegetable or parasite...