No, Facebook does not notify users when someone saves a video. When you save a video on Facebook, the platform generally respects user privacy by not sending notifications to the video's owner or other users involved. Saving a video is a personal action that allows you to bookmark content for later viewing without alerting others. This feature is designed to enhance user experience and facilitate the easy retrieval of saved content within the user's private collection. It ensures a level of discretion, allowing individuals to curate their own personalized library without broadcasting every interaction on the platform.