Had the same thought, but not so much about stability as about how the tensions in SL and NSL change. See, the amount of max difference in tension between a SL and NSL is dependent on the amount of bearing friction. At a certain percentage of that max difference, we would consider the string to be stable.
OK, there's many factors, and I feel I might be rambling. Here's an experiment I thought of. Maybe somebody else's turn to do one. (Still have some firewood to cut if the snow ever melts, and a van with body cancer that is due for inspection.) Make a mock-up of a string and tuning pin arrangement with 1 SL and 2 NSLs. Each segment being a whole ratio of the others like the SL being 12 inches, one NSL being 3 inches, and the other being 1 inch. Include a "Twistometer" gauge like I made for the twist demo and somehow make the friction of the bearing points adjustable. If the string path was a "Z" and the bearing points were tuning pins ground into ellipses, turning the pins would make the bearing point sharper or duller, thereby changing the friction. By listening to the SL and NSLs while plucking, the resulting just intervals that would be heard will tell if one section has more or less tension than another section. (Think about it...) A frequency meter would be helpful for documentation.
To continue rambling, as I know what it is I wonder about, but not confident in expressing it... Ken Burton's book "Different Strokes" on hammer technique talks a great deal about how the proportional relationship between bearing friction and pin torque helps determine the appropriate hammer technique. (Gotta apologize, I haven't read it for a number of years. I am going by memory.) The idea is that if when pulling up to pitch, the pitch stays there when releasing torque, the SL and NSL are at the same tension and the string is stable. This would be because the extra tension in the NSL necessary for the strings to render on the way up, are relaxed the required amount when torque is removed from the pin and the pin untwists. BUT IS THIS REALLY SO? And is there a window of stability, and when there is more than one NSL, would both those lengths end up with equal tensions (I doubt it...), and do they need to be? And one other question is about the residual torque in the pin being a factor when an actual tensioned string is involved. And what about flagpoling?
Ugh, might be better to just get a copy of that university study someone mentioned. But then again, seeing (and hearing) is believing.
Gosh, I hope someone else is up to this challenge...