You might need an annotated edition of The Art of War. Baidu Baike has many false and misleading information 死 here I think is the same with 死 in 死士. Obviously, It's an adjective, so I find a suitable explanation in my Classical Chinese dictionary.This usage is 决心敢死(' [adj] determined and dares to die'). So in the modern Chinese we use today, 死间 as a person= ‘决心敢死的间谍’ It makes sense to me. I read your comments in other answers.I am wondering if you have a Classical Chinese dictionary, online or in print? And how long and how much have you learnt about Classical Chinese so far? The Art of War is not quite a good choice for beginners... Here is a list of common usage of 死 and 间 【jian4】in my dictionary. 死 1.v.to lose life 吾祖死于是，吾父死于是。（是=this） 2.adj. dead 死肌 this word is still used in modern Chinese now 3.n.death 死生，昼夜事也 4.v. to die for sth. 死国可乎？ 死国= die for the nation 5.v. to make sb. lose life.kill 6.n. dead people 7.adv. (拼死命地) do sth as hard as if you 死战，死守 8.adj. (决心敢死的)determined and dares to die 9.adj.won't fail each other even in front of death (至死不负的 ) 遍定死交 10.v. to stop,halt.(止歇) 坏云压城鼓声死 11.v.(熄灭)(for a light)put out,blow out 12.adj.inactive 文章切忌参死句 13.adj.insensible.(感觉麻木的) 手脚冻皴皮肉死 14.adj.(for a place )not easy to reach 疾战则存，不疾战则亡者，为死地。 15.adv.extremly 16.n.corpose 间【jian4】 1.n.空隙；2.n.嫌隙3.n.距离4.v.疾病稍愈5.v.间隔6.v.更迭7.adv.秘密地，悄悄地8.v.乘间 9.v.离间 10.n.spy.11.adv.从小路12.adv.间或、有时13.v.参与14.v.夹杂其间 Yes Chinese is cryptic and classical Chinese is even more cryptic than modern Chinese. But I support you trying to figure out each character's meaning. those trials might fail frequently but it is very meaningful and by learning it people can read really ancient books, that's where I love classical Chinese.You can always pm me if you need help in it.

Wow, I've never thought a foreigner may ask such a deep question. As a native Chinese, I've never heard about the 五间 before. Since you posted your question here, I have checked some information about it. Now let me share my understanding. As you mentioned, 死 refers to death. This kind of spy are ready to die when they are doing their job. Maybe they will be killed by the enemy when they are disclosed, or they might killed themselves in order to confuse the enemy. For your questions in the example, the spy works for A actually. I think the spy knows that the info which he will give to B is false. But no matter he knows the truth or not, the spy will just do what he is told to. Anyway, I'm not a fan of war, maybe I got wrong with many things. But hopefully my understanding could help you a little.

Oh man, it is a hard question. 我也不知道啊！！ I don't think 间 is the spy, more like relationship, like your employee/friends, but you can think it in that way. after I did a research, 死间 is you have to be heartless, for instance, you are lying to your spy to do something, even if it can cause he/she die. however, it is about how to get information from the enemy. so, 有 is 'using'? not sure, but it makes sence in morden chinese. 有因间(AKA 乡间, using your relationship to get)，有内间(bribe)，有反间(misleading the enemy spy)，有死间(be heartless, more like you have to cut you leg for survival)，有生间 (be smart? get the info. without die ) 死间 is a way quite commonly used in monarchy, send a one of the king's daughter to another enemy country, in my opinion.

你在看我们的《孙子兵法》？

死--die 死间-- dare-to-die spy