I'm sure this is completely stupid, but I tried it anyway.
I use a VGA cable to connect my 360 to a computer monitor, and it has the standard red and white RCA male plugs for audio. Naturally, my computer monitor doesn't have RCA inputs, so I wound up using the included RCA to minijack converter to route the audio through the line-in on my PC to get it to output to headphones/speakers.
But I don't want the 360 to be tied to a computer that has to be on to get audio, so I dug out an old RCA PSX audio/video cable and pulled away the two audio cables, which I then cut from the proprietary PSX connector at the end. I then took a pair of cheap headphones that I didn't care if I ruined and cut away the minijack male plug. I stripped the ends of all 4 wires and twisted them together (red to red and white to... green??), and surprise surprise I get no audio from the headphones when they're connected to the RCA plugs on the VGA cable.
Is there any way to make this work or am I just trying to do something impossible because I'm stupid and don't know what I'm doing?
The smart thing to do would have been to get a headphone jack coupler.
Keep in mind that all of these solutions ignore the fact that you're piping line-level sound into headphones, which will be at a set volume (probably too loud) and not sound very good.