You don't need to be immediately reached by phone in these events unless you can actually do something about it. Calling 911 and attending to the emergency trumps calling me at unless I'm close enough to help, i.e. walking the dog, at the neighbor's house, etc. If I have to drive to get there, it's too far; call me after things have stabilized.
If it's a call to break bad news, the last thing you should be doing in the event of tragic news is hopping in a car a driving somewhere while you're an emotional wreck. Racing to the hospital in an attempt to get in "your last words" is dangerous and is not as fulfilling as you might hope. Live in such a way that you're at peace with everyone you care about and last words are not needed.
Also, in my own ability to cope with events, simply receiving news that someone died is the easiest. Being there and witnessing someone die is far harder (or visiting them every day in the hospital until they die...even if you aren't there when it happens), and the hardest for me was performing CPR on someone and the person dying anyways (it helped me to learn later from the autopsy that CPR was never going to help, but it's still traumatic to me in a way that the other events weren't).
In short, real emergencies happen too quickly for a call to non-emergency services to be of any help, worrying about those situations is a waste of your time, and it's possible if you're like me, that actually being there is worse than not being there. Business emergencies are a different beast though.