About two months ago I broke the trap off of a small common venus flytrap. Since the trap had just opened, I got the idea that maybe I could keep it alive by placing it in my small terrarium I had just planted and wait. Well, to my surprise, the trap didn't turn black and die, but it remained green. I took it out of the medium a few times to see if anything was happening with no results. Well, today I took another look and the trap was still green. I pulled it from the medium with a bit of resistance. To my surprise, there is a 1/4 inch long root with a small bud forming.
I will try to get a photo soon.