Today, I was caught by a walker. But, I was actually quite happy about this! No, I'm not crazy. I noticed before the screen faded that a nice new pile of Soul Material had dropped. I went back and aquired the very nice pile of 84 Chaos. Having noticed that, I decided to keep a look out for more drops like it later. As luck would have it (if you can call it that), I managed to experience this again, and got 100 lawful.
Feeling excited with my discovery, I promptly made a new character, killed him, and went looking for walkers...
...And had about 200 of various material types stolen from me over the course of 3 walkers without witnessing any drops. I hadn't known that happened. So much for that.
It looks like sometimes soul material drops when you are caught by walkers, and it is completely new soul material. However, since walkers also drain soul material, making the venture more risky than it first looked. Because of the highly valuable nature of Soul material, I am quite reluctant to experiment with this further.
I think that if you get the soul material, you do not lose any, otherwise you lose soul material. Not that I've had much experience with that. The type lost looks like it is random.
Conclusion: If you feel lucky, give this a try and see what you get. The drops are pretty big when you get them, but so are the losses. Because of the suicidal nature of this excercise, you'll definitely want a new character for this.
If you are willing to help me with the deadly enterprises, including mapping soul material and Wagering against Walkers, send me a mail in game. My Soul Name is Wolind.