How to count non fully walled territory?

Question

I just started to learn Go. I still have some problems to properly understand how to count territory when the game has finished (by both players passing). For example, if the game ends in the following situation, what part of the upper area would count towards black's territory?

$$c13 
$$ -------------
$$|...........X.
$$|...........XX
$$|..XXXXX....X.
$$|..X.X.XXXXWXX
$$|XXXXXXX...O..
$$|..........OOO
$$|..........OO.
$$|OOOOOOOOOOO.O
$$|..........OOO

I know, usually black would just place a stone at L11 befor finally passing but what happens if black forgets to do so? (and white also misses the opportunity to exploit this)

The resources I read about counting did not answer this question for me.

Answer 1

Simple answer: There is no such thing as "non-fully walled territory".

So far as the upper left is concerned, black has exactly two points: D10 and F10. All the rest is not territory, because it's not enclosed. Sure, it's all potential territory, but it only becomes actual territory when black takes that critical L11 point to actually enclose it.

So if your game actually ends in such a state, then black just made a huge 29-point blunder, whether white did anything to exploit it or not.

^{(of course if it's a casual game and you're nice you'll let him fix it because hey everyone makes mistakes but then again you're allowed to be a rule-abiding jerk too because winning is everything it's up to you)}

Answer 2

This isn't really a finished game. If both players passed, then all of the points around E13 would count as dame just like the ones around H8, and wouldn't be territory for Black. This wouldn't happen in a serious game, so in a beginners' game, you would notice the problem during the scoring and probably just fix it.