How can low cholesterol cause mortality?
What you have asked for is a causal answer to correlated findings. There is no cause-effect evidence (at least from my searching) showing low cholesterol will indeed cause stroke. Associations like this are dangerous in the sense that we shouldn't think that one causes the other. But, we can speculate on how they are linked, which is always fun.

I'll be going off my understanding of cholesterol transport and will include the reference at the bottom. Essentially, cholesterol is used in the cell membrane to change the permeability of the membrane. The more cholesterol, the less permeable the membrane is to water. However, this also changes the physical properties of the cell membrane, making it more rigid and structured. If I had to guess (which is again PURE SPECULATION) I would think that decreasing the cholesterol to the point of a dangerous level would increase the cell permeability of vital cells, the most sensitive would be neurons who depend on ion based signaling to perform primary functions. Since ions are very small and easily pass through the membrane if the membrane is leaky, they might be the first indicator that the something is wrong and the membrane isn't strong enough. Again, purely speculative with no evidence. An experiment one could do is examine the amount of cholesterol required in a cell to keep ions from crossing the membrane and see if there are any other effects that occur within or around the cell before ion passing. If you aren't in this type of research yourself, maybe you can fund it! 

Source= Cassarett and Doul's Essentials of Toxicology. Textbook, 12th edition