I too am sorry to hear of your loss.

I have had an experience in a similar situation.

I and a few other members of my family were booked on restricted tickets to SFO last March. My mother in law was one of those due to travel.

A couple of months prior to depature, her partner (who was not due to travel) who has cancer took a bit of a turn for the worse and in order to stay and care for him, she was unable to travel.

I rang the BAEC and immediately asked to speak to a manager and explained the situation, when asked why, and said that I wanted to speak to someone straight away with the authority to help me rather than have to relay the story time and time again.

I explained the situation to the manager calmly and asked for his help despite knowing I was on a resticted ticket (non-refundable) and he said to fax through a doctors note confirming the situation, and once this had been faxed, I had a miscellaneous charges order (credit note) through in the post for the non refundable element of her ticket. I think maybe there was a small fee to pay.

So I would certainly suggest speaking to BA on this. I would expect that they should (and know that the could) refund the non refundable part of your ticket by means of a credit note.