Mystery Romex in junction box
It's not unusual to see an unused wires folded up in a box with the ground connected and the other conductors capped.  Unfortunately it's very rare to see anything marked or labelled to help the next guy figure out what's what.  

This one's a little different in that it's clipped short on purpose - someone wanted to discourage trying to use the wire - and the wires are not capped.  

I'd cap the wires and leave it alone.  Turn off the breaker for the light circuit, test to see if the short wire is live, and if so find and turn off that breaker.  I'd peel back the jacket 1/2", carefully strip 1/4" or so off the black and white, and twist on a small wire nut.  

Tracing the wire to figure out where it goes and the rest of the story could be a bit of a project, and there's nothing to indicate any hazard, so I would not bother.