Looking quickly at your question and drawing.... I would say that is something you do not want to do. I am assuming you data is attached to your geometry so any editing would have to occur on the complete geometry segment. That said, and the fact that nothing is impossible, one way to accomplish your desire would involve:
1. Split your geometries at the border of your AOI.
2. By programmatic means lock the geometries that are outside of the AOI (if segment outside of AOI polygon then don't allow edits)
HOWEVER, I would highly recommend you do not go down this path. In time your data-set will become unmanageable. The best way may be user training to not edit outside of your AOI's