Those are a bit harder to find since they also must include all of the electronics that a telephone contains. But yeah I understand what you're looking for.

It strikes me that the sort of thing that you need is *almost* an answering machine. All of the bits are there (including microphone input), it's just a question of how/when each bit of audio signal gets routed.

I'm surprised your video conferencing system doesn't already include this kind of thing. Sounds like the video conferencing system is (deep inside) just a PC, and all it would need was a voicemodem card and some software jiggering.