Xbox 360 – Fixing Red Light Issues on Power Supply at Startup

Actually it doesn't do anything amazing. It just simply cuts the power. Unlike a computer, the XBox doesn't have any major work that needs to be done when switching off. There is no data that needs to be saved, and there is no processes that really need to be quit cleanly.

The XBox was built with a different concept in mind then a PC, and therefore, just pressing the button, pulling the power or even using the control to shutdown the console, all do the same thing, cut the power. All important data on the XBox is saved at the point it needs to be saved, and it hardly if ever, keeps important data in memory.

From comments

At the time of writing the answer I forgot about the scenario of active downloads. If you have configured you XBox 360 to continue downloading if when off, the XBox will go into a sleep state when using the controller to switched off, with the exception of pulling the power.

Generally speaking those adapters are of low quality and will most likely not invoke a fail-safe to save your device. I noticed the slim adapters are of a much lower quality then older adapters that had built in fans and a ground. Without a ground it had no where to send the electricity and more than likely it simply passed it on to the device. The fact that you had to unplug it and it didn't shut down automatically is a REALLY bad sign. Generally devices can handle variances in voltage but in your case it was a significant variance. Did the xbox light up or did the touch button make the ding? If so your chances it survived are even less since it was obviously drawling power from the device. You probably have a very small chance it survived but the only way to know for sure is to test it this time not a on 240v outlet! Best of luck.