Our first husky did that ALL the time. It was embarrassing, for sure! You have this beautiful husky with a weird, crazy haircut on her tail. We looked into it for years and assumed it was boredom or pent up energy while in her crate. She would occasionally do it after she was allowed free roam in the house. She never did it when we were home (that would rule out skin itches of any sort - allergies, fleas,... - if it were those, she would have been gnawing more).
I would check for that lone flea or flea bite and watch to see if she nibbles when you are home.