This sounds like a TV application...I'm not sure how TV automation works or what devices it would use to accept or output closures.
For radio, as TomT says, the Measurement Computing stuff can be used to interface closures to a PC through USB. Their stuff has drivers built in to BSI Simian. If you want to interface it to something else, you can probably roll your own program using Visual Basic or C to poll the inputs and send a command to some other automation package.
I'll give an example of how this sort of thing can be made to work...I wanted to do this sort of thing for an LPFM station that I volunteer at doing sports. Before being able to secure donated studio space, they were operating from automation at the transmitter site. We had a POTS line put in and I found a used dial-up remote control system that could generate relay closures or patch the phone line to air in response to DTMF commands over the phone line. Their automation had no provision for remote control, but I found a program called AutoHotKey that lets you generate self-contained executable macro files that can send commands to programs via keystrokes or Command ID. I hacked together a VB program that would poll the Measurement Computing device and -- depending on which pin the closure was on -- trigger a macro to tell the automation software what to do. The system is somewhat kludged together (on top of the music automation program, we also are using a different freeware cart player to fire the open/close carts, and Winamp to rotate the underwriting spots), but it seems to work!
Bottom line -- it can be done, but you may have to roll your own drivers for the GPIO part. That's something that's done a little easier if you know a good software guy.