Camera FollowPlayer Unity code example
Example: linerenderer follow camera unity
You can render the line using a dedicated camera. Use .depth to control the order in which cameras render (i.e. render the line on top of -everything-), and .cullingMask to define what each camera renders (or not).
http://unity3d.com/support/documentation/ScriptReference/Camera-depth.html
http://unity3d.com/support/documentation/ScriptReference/Camera-cullingMask.html