I wonder is it possible to rig alsa or/and pulseaudio so that audio output to left stereo channel will come form one process and to the right channel from another process?
Since both ALSA and pulseaudio support dynamic mixing of multiple audio streams, you could just have two audio source processes that would output full stereo audio, but with one channel containing only silence. That should work with no modification in your sound system configuration.
Using two music player instances, for example, you could just tweak the Left/Right balance control, so that the appropriate channel of each instance would be fully silenced.
Why do you want to do that, anyway?