What is the purpose of power going into a Phone Receptacle?
From your back side picture it is apparent that no small gauge low voltage wiring goes to the box with the four prong plug. So unlikely that the plug was used for wired phone service at any time in the near history.

It is almost sure that someone at one time wanted to power some ill conceived device with power through a four prong plug. If you open up that box you will undoubtedly find that some pins on that plug are wired into the power circuit that passes through that electrical box. 

Sometimes it is just hard to understand some of the schemes that folks will dream up and cobble together, whether it is safe or not.