Allow Grieving Families discounted Airfares to Honor their Deceased

I believe that when a family experiences a death in their family, US Airline carriers should allow heavily discounted fares ( or free airfare) to families provided the family can provide adequate proof of the recent death to the airline. With the Airline Industry making 19 Billion dollars in profit in 2013, allowing greiving family members a couple of seats for a heavily discounted fare or free would barely make even a scratch in their operational budgets.