Empty texts are being sent periodically to specific contact?
I figured it out. I also have Avast Anti-theft set up, and for some reason all of the messages I send or receive are being forwarded to this contact via binary which is why the messages are empty and why the contact's iPhone is ignoring them. 

In short, a bug with avast is the cause. Going to have to give their support a piece of my mind for driving me crazy for two weeks.