Starvation has been used by Hindu, Jain and Buddhist monks as a ritual method of suicide. Albigensians or Cathars also fasted after receiving the 'consolamentum' sacrament, in order to die while in a morally perfect state.Carradine apparently chose strangling. It's possible he was afraid someone would find him and force-feed him. If ever I kill myself, strangling would be my second choice. (I had once thought I would try to get lost in the snow, but people don't simply "go to sleep" in the cold. Sometimes they take off their clothes, which suggests they feel like they're too hot.)
The explorer Thor Heyerdahl refused to eat or take medication for the last month of his life, after having been diagnosed with cancer.
A hunger strike may ultimately lead to death.
Possibly of interest: More Patients Choose Starvation Than Assisted Suicide - Health News Story - WFTV Orlando
"We were surprised that patients who chose this means to hasten death were, according to their nurses, more peaceful and suffered less in the last two weeks before death than patients who choose assisted suicide," Ganzini said.