Pretty much the same as everyone else's. Just wanted to point out that immortality wasn't an innate trait of the NE, but something that was granted to them via blessing.
The thing is - we really don't know.
All we know is that Kil'jaeden sent Illidan in W3:TFT to blow up the Frozen Throne, because the Lich King rebelled against him. I don't think it was said whether this was purely an act of vengeance/punishment, or something done due to fear of the LK complicating things in the future.
I'll reiterate my point though - seeing as KJ created LK, it's completely possible that he has intricate knowledge of LK power and thus deviced some sort of way of disrupting his magic or control of the undead.