Added in iOS 10, Emergency Bypass is a way to ensure that you will always be alerted by a certain contact’s phone calls and/or texts, even if the phone is in Do Not Disturb mode and even if the mute switch is engaged. But this feature is a little bit hidden, so here’s how to turn it on.
You can also exclude certain groups of people from ignoring by setting "Allow Calls From" under Do Not Disturb preferences. It does silence messages though…