My invention would have a strong but flexible cord with one end going through a loop on the case on the personal electronic device, and the other end going around a persons belt—attached either by a keychain—type device on the belt, or, going around the persons belt loop.
I have not seen anything like this and by simply manufacturing the personal electronic device case with a loop at the bottom and a strong but flexible cord, thieves would not be able to grab and run with it particularly on the subway.