No matter how careful you are when using your phone, it can still happen. I'm talking about that horrible moment when you drop your phone and you end up with a shattered screen. If you’re lucky enough, the touchscreen still works, as just the glass covering it is broken, but there are users who can’t use the phone at all.

Let’s say that you are among those whose phone is not worth repairing and you decide it’s time for a new one, so you need to recover all your files. But how on Earth can you enable USB debugging with a broken screen, in order to transfer them?

How to enable USB debugging using ADB Commands

Tthese are the steps you need to follow:

-Install ADB on your PC
-Connect the phone to a PC, using a USB cable
-Boot your phone into ClockworkMod Recovery, by pressing and holding the Power Button + Home Button + Volume Up or Down, depending on your phone
-After loading ClockworkMod Recovery, check if the ADB connection is running, by opening a command prompt on your PC and typing adb devices
-Start backing all the data on your phone, by typing in the same command prompt adb pull / data / media / clockworkmod / backup ~ / Desktop / Android-up

https://www.unlockunit.com/blog/enable-usb-debugging-broken-screen/