I've known this for a long time. A quick google confirms that many people think the same.
Basically, that when shutting down a cell phone, the antenna still communicates with the tower. Triangulation will still work, as well as some other stuff.
Only when the battery removed, is a cell phone "really" shut down.
Not that I care but it's interesting to know why!
If possible, please provide primary sources - it's time to shut all the myths around this down!
Update, the following question has been suggested: What is the fastest way to shutdown unrooted Android phone? Obviously, this is semantically NOT equal. The answer there, despite being a very detailed answer, does not provide the reason WHY the baseband processor remains ON.
For a technological feature to exist on perhaps Billions of devices, there must be a need for that... Especially since it drains battery and costs cellular tower bandwidth.