Hmm... Someone should collect all the death-quotes from the entire book, and put them in one place (both the "Collected on's" and the ones from random people dieing.)
That would probably help with our theorizing.
Anyhow, interesting correlation between the wavy-headed spren and the amount of death. But I don't think they are death-spren, consider how Jasnah was able to soulcast with a fake soulcaster well before she went to study in the palanaeum.
However, I strongly believe that they have something to do with death, and truth. Consider: The only person we know much of who has attracted one of these spren is Shallan (we don't know much about Jasnah, unfortunately). These spren take you to Shadesmar (which is likely the cognitive realm. It could also be the spiritual realm though, unless Brandon said otherwise).
Now, what do we know of Shallan that would make attract these spren to her? She has a shardblade, is (or rather, was) living a lie, and she murdered her father. Unfortunately, this doesn't tell us much except perhaps the murder. Maybe these spren are attracted to killing? Unlikely, as there would be many Alethi soldiers with spren hovering around. Perhaps these spren are attracted to something else? Deep, emotional scarring? Unfortunately, we don't really know enough. I can't make heads or tails of it, really. What do you guys think?
Well, we don't know what attracts these spren, but perhaps we can find out what these spren are. There are three options that stand out, Truthspren (note how they asked for one truth to enter Shadesmar), Soulspren (they allow you to soulcast, they have something to do with death.) or Shadespren (they give you access to Shadesmar, and they aren't really visible in the physical realm, they are only visible through the cognitive realm).
Can you guys make some sense of this? I've about run out of ideas here.