EMERGENCY CONTACTS should be able to reach the phone owner, no matter what. When my phone is on vibrate, silent, or Do Not Disturb, I want my EMERGENCY contacts, which includes any alternative numbers from which I may call my phone when lost, to bypass the privacy feature in the method/s I so choose.
If I want certain or especially EMERGENCY contacts' texts to pop up and/or my phone to vibrate, and/or my phone to ring at the loudest volume when on silent, vibrate, or do not disturb, I should have the option of this LIFESAVING feature. It could also help during immediate theft.
This very day, I lived through the LIFE ENDANGERMENT need for this feature. I had my phone on vibrate in my pocket, and did not feel nor hear it after half a dozen texts, and over half a dozen calls in the same hour. One of us could have died!