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.