How do music players survive hot reboot? When I do a hot reboot, everything is killed and restarted, but I never ever experienced any interruption in music playback. How?

System: Samsung Galaxy S (ICS)
Music Players: Stock music player, PlayerPro, Rocket Music Player
The typical implementation of a "hot reboot" does not actually shut down the OS and restart it (see What does Hot Boot mean? for related discussion). In essence, it's killing the UI and other foreground processes, then restarting the UI components, making it somewhat analogous to restarting the X server on a *nix machine. 

The music player spawns a background service that actually handles playback, and services simply aren't interrupted in the hot reboot process. Using the *nix analogy again, restarting your X server typically doesn't kill your daemons, but it will stop any currently running X applications. It's a similar principle on every hot reboot implementation I've seen.

Now I should probably also qualify this with a disclaimer that this is based on my understanding of one such implementation of the "hot reboot" feature. There may be others that do it differently, but since this is not a standard/native feature and it's generally not documented anywhere you'd likely have to reach out to the developer of your particular app or ROM for more information. Heck, this may even vary depending on the music player you're using - the above is just my analysis based on the limited information I've found available on the subject.