Not quite the same situation, but eight years ago QANTAS staff went out of their way to make sure that, if it were possible, I would get to my mum in Perth before she died. A ticket was made available for the next day's flight. Amongst other things an inflight message was passed to me by the CSD telling me who was going to be meeting me at the airport (a very good friend of the family) and I was first off the aircraft, escorted through Immigration and Quarantine and my baggage was fetched for me. I was treated with great care, consideration and kindness. They could not have done more to help but sadly, mum died two hours before I landed.
You might imagine that the return trip would be routine, not so. I was booked to return on QF5 via Singapore and Frankfurt. The flight hadn't even left Australia when I landed in Singapore so everyone was being sent to hotels for the night. I remembered a snippet of information from when I had been planning my next trip, which was that I thought the BA flight from Frankfurt to Manchester was the last one until Monday (I was flying to Manchester on Saturday.) The Ground crew checked for me, found this was correct, and promptly started searching for a seat for me to get me home earlier. They also provided me with a phone card so I could let the necessary people at home know. I discovered during the course of my conversation that they felt I had had enough to cope with over the previous week. The staff went out of their way and I found myself on a QF flight to Charles de Gaulle followed by a BA Fruitbat, sorry, BAe 146, to Manchester where I arrived a mere two hours later than scheduled.
As I said, this isn't the same as delaying a flight, BUT, as someone who had had a lot of sadness and stress over the previous few days, it was much appreciated. Please continue to do what you can for those in genuine need, they might not be able to tell you at the time, but it will be appreciated. yes, I did send a letter of appreciation to QANTAS, it was the least I could do.
Speaking as a passenger, I would happily wait for someone who genuinely needed to get somewhere for similar reasons.