The Hacker News has a nice article about it Android Malware Can Spy On You Even When Your Mobile Is Off or you can read the original AVG post Malware Is Still Spying On You Even When Your Mobile Is Off
As the AVG blog explains:
The malware affects versions of Android older than v.5 (Lollipop) and requires root permission to hijack the shut down process.But beyond the obvious problems with a malware spying on you, recording you, and sending your data to Chinese servers, it can be making Premium Rate SMS or calls without your knowing it.
After pressing the power button, the phone displays an authentic shutdown animation, and the phone appears off. Although the screen is black, it is still on.
While the phone is in this state, the malware can make outgoing calls, take pictures and perform many other tasks without notifying you.
The Hacker news article points this out:
PowerOffHijack malware has ability to silently send lots of premium-rate text messages, make calls to expensive overseas numbers, take photos and perform many other tasks even if the phone is supposedly switched off.The article also has good options for removing PowerOffHijack and preventing it from getting on your phone