The fine line between the teachers responsibility and the parents!

I truly believe that a teacher is a teacher 24 hours a day and 365 days a year. Our job never ends and we always have the best interest of all students as a priority. When it comes to internet safety, I have to wonder where our job ends and the parents' begin. We, as teachers, can only do so much to teach our children internet safety and to prevent cyber-bullying, however once they are out thoses school doors our hands are somewhat tied in terms of what we can do. When the cyber-bullying is happening from a home computer, I believe that the parents play a key role in being responsible for this. This was an issue this year at my school, but what is a teacher to do when this is happening outside of our walls? Surely we do our best to educate about the subject and to prevent it as much as possible, but where does the teachers' responsibility end and the parents' begin?