Myth: Oda stated in an interview that Crocodile and Arlong were executed.
Fact: An old rumor based on unfounded sources that claims Oda stated in an interview that Crocodile and Arlong were executed. However, no such interview has been shown to actually exist. When Luffy defeated Crocodile, he was knocked through the bedrock and fell to the ground outside the temple, wounded. Same goes to Arlong whose nose was broken and his castle fell on him.
But in the Miss Goldenweek side-story, Crocodile was in fact alive in prison and later seen to be still alive in Impel Down, exposing the interview to actually be a myth, Hatchan also confimed that Arlong was in prison as well.