AA does offer these fares. I used one 2 years ago to attend a funeral. Getting them can be difficult though. An AAngel in DEN had to "work the system" to get the correct fare code (K I think). She broke a few rules, but thats a different story. From AA.com:
"Q: Do you have any emergency or bereavement rates/discounts?
A: We do offer emergency fares for different situations. You cannot obtain these fares on AA.com and will have to contact American Airlines Reservations."