Yes, the end of the story isn't necessarily the end of the editing. And there are many ways to call the editing complete. When you can't find anything more that you or your alpha and beta readers think needs fixing. When it's accepted by an editor and published. When you can't tolerate any more rejections and begin another story. And so forth. Striving to make something perfect is an asymptotic struggle, but we all have our ways of trying to give our readers our best writing. Here's mine. First Reading > ignore spelling, grammar, punctuation, sentence length and word choice so the story itself becomes the center of my attention. Second Reading > with the plot and the characters roughly established in mind, evaluate the arc of the story from its title to the beginning, middle and end. Third Reading > unleash my ferocious editor by humiliating myself with cruel remarks about technical things like spelling, grammar and diction and literary things like dramatic suspense, unrealistic dialog and endings that just plain suck! Huckleberry Finn was certainly done with his story when he said, "And so there ain't nothin' more to write about and I'm rotten glad of it 'cause if I'd a know'd what a trouble it is to make a book I wouldn't a tackled it and ain't a goin' to no more."
This is my answer if we are talking Novels. Short stories tend to see four or five minor versions (major versions are rare, I tend to know what I want from the start). Then I'll pass the 'code' to all the readers available at the time, and at last... I'm forever through with them. Yes, I've said forever. Honest. To keep track of my progress as a writer, I sometimes read those Stories after months or years, and even then I rarely spot anything I'd like to change, probably because I'm just reading them as a reader, not as a writer. They don't 'belong to me' any longer.