My uncle died a few weeks back and my mother had to postpone her trip to LAX on AA by a week - she was told to take a letter of confirmation to the check-in desk on the rebooked flight and all she had to pay was the difference in fare as it had increased in the week - it was abotu $100 - the change fee was waived.
My mother has no status on AA and it was in fact her first time with them - she very much enjoyed MRTC.