How do anti theft apps deal with the thief simply turning off phones? https://bestidtheftcompanys.com/2014/top-20-free-apps-to-protect-your-android-device/

There are so many anti theft apps and devices out there, however, all of them can be defeated by a simple trick—just turn off the phone. Any apps that make the phone scream when stolen will just be silent. How do anti theft apps work with turning off phones? Do they make the phone scream when being turned off while being locked?
Yup! :) , you are right about this.But in XPosed Installer there is an app known as APM+ ( Advance Power Menu Plus ). This has a feature known as Fake Power off. By this your phone can pretend to be off, but in reality it would be working stealthily and every approach from real owner can be done.
Like this there are also other option which comes in handy.

As requested: 
Anti-theft Helper™
Note: Actual effect of anti-theft is NOT guaranteed.
• Stop anyone from turning off your phone, enabling airplane mode, etc. when the device is locked by hiding any power menu items when the device is locked. In this way no one can stop device trackers like Android Device Manager from locating your phone by turning off the phone, disabling mobile data and so on(removable battery not taken into account)
• Show a warning to deter thieves.
• Fake Power Off - When you have this option enabled, trick your thieves by "apparently" turn off the phone, but the phone leaves running so you can still track the device (various options and strategies available for fine tuning the effect. Result may vary on different devices)
• Password protection - Lock power menu items and/or the app itself with a password. Apart from thieves, it is also ideal when your phone is on display.

Xposed Module Repository For APM+