On a non-rooted android device, I can navigate to the data folder containing the database using the run-as
command with my package name. Most files types I am c
I couldn't get anything else to work for me but this:
adb shell
run-as package.name
cat /databases/databaseFileName.db > /sdcard/copiedDatabaseFileName.db
exit
exit
adb pull /sdcard/copiedDatabaseFileName.db /file/location/on/computer/
The first exit is to exit out of the run-as, the second exit is to exit out of adb shell to do the pull.