The worst time to travel isn't during the holidays, or when an airport is plagued by weather delays - it has to be when you are flying for a family emergency. I have flown out to family funerals, and when my father had a massive heart attack, and the common thread is that the emotional edge makes air travel that bit more challenging, that bit more difficult.
It's important to note that not all airlines offer special fares for funerals or imminent death. The ones that do have different definitions of who qualifies as a family member for the bereavement or compassionate airfare. And finally, just because it is discounted, does not make it the cheapest airfare available. Usually they are more flexible though.
Also, what happens to the frequent flyer miles for a person who has passed away? Airfarewatchdog asked this question and came up with a chart for several airlines regarding how frequent flyer miles can actually be bequeathed to someone, including what is required and what costs may be incurred to do so.