When my sister died in an accident several years ago, I made an award booking to go back for the funeral. Out if F, then back in J the following week.
I called the day before the return flight to ask if I could possibly change to a couple of days later, as my Mum was still an absolute mess and I didn't feel that I could just pick up and leave.
I don't know if it was entirely down to the situation as presented, but I was allowed this change without any question or hesitation. So it looks like there is some flexibility in the policy. My eternal thanks for that, BA. ^