Update 31-01-17 - We have carried out a series of tests and managed to replicate the issue.
LibreELEC -> Raspberry Pi B+ -> DAC HAT No issues
LibreELEC -> Raspberry Pi B+ -> DAC Zero No issues
LibreELEC -> Raspberry Pi Zero -> DAC HAT Blank screen
LibreELEC -> Raspberry Pi Zero -> DAC Zero Blank screen
Other Kodi based OS are working fine with all of the combinations above.
This happens when selecting the card under Settings - Audio, the screen goes immediately blank despite the rest of the system being still up and running. No changes with or without dtparam=audio=off.
Can somebody from LibreELEC please help?
Unfortunately I don't have a RPi Zero (they still seem to be impossible to get) so can't test myself.
Could you run a test with the latest Milhouse build? LibreELEC Testbuilds for RaspberryPi (Kodi 18.0)
Testing with a kernel 4.10-rc Milhouse build would also be interesting LibreELEC Testbuilds for RaspberryPi (Kodi 18.0)
If they also fail please post the output of tvservice -s before and after the display blanks and please also post the dmesg log after display blank.