A person who is 'living on the edge' is usually referring to a person who is drawn to or is constantly in a dangerous situation. A person who skydives, wind surfs, in a violent gang or has a career with a lot of danger. But it can also refer to a person who is living with bad decisions....doesn't pay bills, is a drug addict and so on.
These people are closer than usual of falling off the edge of a cliff because they live on it. :)