Exchange emailing outside

Over a year ago, the guy who had my job before me decided it would be a good idea for us to have an isolated Exchange server that could not send or receive emails with the rest of the world. All external communications are handled by a hosted POP3 server.

The president of the company wants to keep the emails set up this way, but today we realized that people who do not have external email are able to send emails to the outside world, though they still cannot receive them.

My task is to block the emails from going out again, but I have no idea where to begin or even what might have happened to change this.