In the situation such as a family loss or accident, many airlines offer bereavement fairs. What is on offer ranges a lot, from having no discount to a substantial one, but often with the major benefit of not charging for having a open ticket, or changing flights suddenly. What they require as proof also depends on the airline, ranging from a letter from a funeral home or a copy of the death certificate.
Here is a list of Airline Policies, with regards to Bereavement Fares. List is in no particular order, nor complete;