Of course, neither can the hospital or nursing home keep the patient there against their will. Therefore if someone insists on death by starvation/dehydration, they'll have to get transferred from Sacred Heart Hospital to "Skinny Sam's Starvation Emporium d/b/a/Compassion and Choices" for the final wretched days.
As far as I know.
Some better-informed FReepers is invited to jump in and correct me if I'm wrong.
I’m not sure you could order yourself starved to death, legally, anymore than you could order yourself to be sold into slavery (specifically a legal impossibility).
But have no fear, the death advocates are working on it.