MLB Rule: Is a Runner Out After a Catcher's Overthrow?

Question
Batter / Runner hits a ball a few feet in front of Home Plate.  Runner is inside baseline in fair territory.  Catcher makes poor throw toward first baseman overthrowing him by a large margin.  Runner was not struck by ball and runner did not inpeed first baseman's attempt to catch the ball.  Is runner out?

Answer
From the way it sounds, I don't think anyone should be out. But then again, I'm not sure if I'm exactly reading it right. To be completely honest with you I can't give you an exact answer, from my baseball knowledge he should be safe and it should just be an error but I'm not positive.