Technically, your profile picture is always public so people can recognize you. However, users can use a Profile Picture Guard to prevent others from viewing it in full-screen, sharing it, or downloading it directly.
: Navigate to the Accounts Center (or Your Facebook Information on older layouts) and select Download your information . Download Facebook Private Profile Picture
Extensions can often "grab" the unique Facebook ID of a profile to find the source image URL that the standard interface hides. Facebook ID Grabber Technically, your profile picture is always public so
Quality might be limited to the preview size if the profile is strictly locked. Download Facebook Private Profile Picture