music stops

By pressing that power button, aren't you telling your phone that you might want to turn it off?
That might be why your device stops playing music or your files!
And if your listening to music, why would you want to return to your locked screen?
Or do you mean your home screen?
To return to your home screen, just use your home screen icon or button, but that might stop the music also!
It dosen't sound like anything is wrong with your device! It's just obeying your command!

When your phone goes to sleep your suppose to wake it up with the home key not your power button!
Pressing the power button when the phone is all ready on, is telling it you want to turn it off!
That's why it shut down your music app.

For the last time,
When your phone goes to sleep,
Do not use your power button to wake it up! Thats telling your phone you want to turn it off.
Use your home key to wake up the device!

Most phones have a black key right below the screen. That is the home key you use to wake up a sleeping phone.
However I understand that the Moto E4 has a fingerprint scanner in the same place! (Just below the screen in the center) that should be where you press to wake up your device!
If that dosen't work call Motorola's customer service and ask them how to wake up your phone.
Note; I found out about the fingerprint scanner on the internet. You could have done this yourself!

Do this; go onto You Tube
Punch in search; how do I wake up a sleeping Motorola E4.
There is a video that will explain how to go into settings and program your device to wake it up with the double tap method.
Again if that dosen't work call Motorola's customer service that's what they are there for!