Zec can't allow any "loose ends" at any level, and if anyone refuses to accept that, or can't demonstrate their "rareness" to do what's necessary to survive, then they will be killed.
What is the meaning of this sentence from Jack Reacher synopsis?
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A minor unresolved problem or difficulty, especially a final detail preceding the completion of something
However, I think that loose end also often refers to a major problem, not just minor ones.
In this context, we need more clues as to what rare means. It is a usual dictionary meaning. Earlier in the text, it says
He wondered what Linsky would do to survive, to prove that he's among those people who are so "rare" that they would do anything to survive and thus would always prove that they are somehow useful in the world. He then orders Linsky to prove his worth by chewing off the fingers of his left hand.
So it appears that to be rare refers seldom occurring or finding people who are able to anything to survive, including gruesome, gory acts like chewing off their own fingers.
So I believe that the author is concluding that Zec cannot allow any problems to be left unresolved. Further if someone cannot prove that they are among the uncommon group of people who will do things like chew of their hand to survive, then they will be killed.
However, it is not clear (to me at least) whether the author is suggesting that the Zec is specifically referring to Helen, her father, or other people.