Sorry, no reference I can find gives any indication why the (没)有 is even there... does anyone have any insight? (Is it some sort of tense thing? Cuz that's what I looked for and literally nothing lists it...)
You don't need to put 了 at the end of the sentence, just say 他沒有出去 (he did not go out).
But if the sentence is affirmative: ''He did go out'', then you have to put 了 and say 他出去了。
了to me sounds affirmative to a fact - what is already happened.
Everyone's asking about why there is 没有.
I would think it's because 出去 takes the form of a noun in Chinese.
去 is a verb, but maybe 出 makes it like a gerund (a "going out").
That's my best guess - native speakers, please reply and explain!