First the good news: There are ways to navigate your phone with a broken screen, or even without a screen.
The bad news: You will most probably have to setup these ways before your screen breaks.
For reference … I have personally checked out the following:
In case of encryption and if you have to start/ restart the phone, you’ll need a USB keyboard to enter the password. (A wireless USB mouse/keyboard combo will work, too.)
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DisplayLink
You’ll need a USB mouse.
I followed the hint given here and bought this USB adapter thingy.
It works, but you have to install an App on the phone first and probably give it some permissions (don’t remember).
However, I found to get it working with the screen taken off (my only idea of simulating a “broken” screen) was hit and miss because of my phone being encrypted. Sometimes I managed to enter the encryption password blindly, and then the phone booted and the DisplayLink App correctly worked via HDMI to do the rest … but sometimes I failed and had to restart the process until I succeeded. -
MyPhoneExplorer (Windows only)
(In case of encryption you’ll need a USB OTG adapter to connect the keyboard.)
With MyPhoneExplorer you can remotely navigate your phone on your PC when it is booted and plugged in via USB.
But the MyPhoneExplorer Client App has to be installed on the phone.
And when you start this screen mirroring for the first time, you have to allow this via a requester on the phone, and you would have to disable this requester for future use at this point (there’s a checkbox in the requester).
In both cases I experienced very, very severe lag when moving the mouse pointer with a disassembled screen (when with the screen assembled both solutions worked totally fine).
This means that there could be problems unlocking the lock screen if this behaviour might be the same with a broken screen instead of a disassembled one.
If so, swiping a pattern will probably not work.
And swiping up to enter a PIN will probably not work, but double-clicking on a notification will get you to entering a PIN luckily.
So use a PIN for the lock screen, not a pattern. And see to it that you can generate a notification yourself on the lock screen (new mail or message, missed call etc. …).