Apps stay in background even after turning the phone off I generally see this in all the Android phones I ever had. I have certain apps in the background and then turn off the phone. If I turn it on again the next day these apps seem to still be in the background. It could be any app, Google Maps, Candy Crash etc.

Why does this happen? Don't Android phones turn off completely? Do these app really stay in the background?
That is the default behavior of Android from Lollipop onwards. See this blog which talks of that ( Recents (or Overview)). It is only a list of apps that you used is shown and it doesn't mean that these are running after reboot, so it shouldn't be a concern (unless you want to hide some app or web page that you visited). You can check running apps from settings and you would see that these are fewer than what you see in the overview

Only on earlier versions they would be cleared on reboot