once per session, not once ever
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I think you miss the Point of my Argument. Sticking to my Dice example, i’m not here to argue the probability of getting the number you want after doing 50, 100 or even 1000. It’s obviously that the more often you roll, the more likely atleast once you get the number you want, because you have more chances. The flaw in Logic which i see here, and that’s why i argued they way i argue, people like op tend to think that it affects the probability of the dice roll itself, which isn’t the case. So call it universal bad luck or whatever… it doesn’t change the fact that if you do 100 or 1000 rolls even with a chance of 1 out of 6… that there is the possibility that you might never roll the number you want. Unlikely, but still possible…
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I just wanted to point out that you shouldn’t in my opinion give examples of events that are as less probable than the fact the Earth is flat or that you disappear as I’m writing this post due to some random quantum fluctuation. The probability of not getting Kilian 1000 or even 100 times is so low every person should make a bug report in an instant if it happens to him and (s)he will be right 99.9999…% of the time. Or it could be easily considered a physical law that this is impossible. No point in assuming we live in a reality where anyone could ever have such a bad luck in Grim Dawn. Or for example any human being could ever get 1000 heads in a row by tossing a coin even if we all tried. That was my point you missed.
Maybe it’s the Kylrian Soul that disappeared due to quantum fluctuations?
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Another one 
Feed Maya Ice Cream if you want better luck with stuff.
Do note however that there is a chance your luck might remain the same or go lower after the process. But do not be disheartened and keep feeding Maya Ice Cream until your luck goes back up.
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You can greatly reduce the tedium of farming Krieg by ensuring the difficulty is Elite, and farming can be done as soon as the bosses are lvl 75 or above. Like Malawiglenn said, you can do the ~50-65 kills necessary for that 95% confidence of seeing them drop in a few hours. Farming is best done on a character with high movement speed, and if you have FG expansion you can have 2 movement skills with your mastery choice.
Thankfully, Krieg set drop mechanics are far more generous than the vast majority of other legendary gear as it can be target farmed, otherwise your chance of acquiring them would be far lower.
It has been a very long time since I played multiplayer but aren’t drop rates independent for each player (as long as shared loot is off)? with a 25% drop rate, and the run to Kilrian only a few minutes, you should have seen it by now.
If not, just do ~3-4 runs every time you fire up the game and you will see it eventually. I am sure it has been frustrating but a 25% drop rate is not low.
Im pretty sure that he didnt have the loot filter configured properly and didnt have the option to automatically pick-up components enabled either, since after @Ceno mentioned it he goes into radio silence.
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