There were eight people murdered by inmates on Alcatraz. Five men committed suicide, and fifteen died from natural illnesses. The Island also boasted it's own morgue but no autopsies were performed there. All deceased inmates were brought back to the mainland and released to the San Francisco County Coroner.
From what we understood the morgue was not used by the prison but used before it became a prison for prisoners of war.
Not anymore
From a tour of the prison I recently took about 2 weeks ago, the said they cremated those who died.
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