I think maybe you mean the style rather than the stigma (the style is the long tube with the stigma at one end and the ovary at the other, all comprising the pistil)?:
http://www.daylilies.org/ahs_d...
The style normally curves so I assume you mean more than normal, and spiraling of the style where it wasn't earlier in the day is a sign of an aging flower according to some research in Russia. Can you post a picture of what you're seeing? I think I've seen them start out that way and put it down to a developmental deformity but don't really know why.
Incidentally, that same research found that native daylilies had stigmatic fluid between one and a half and two hours after the anthers opened.
