I doubt very much that the airline was not selling at the highest possible fare but at the lowest fare AVAILABLE for the journey

This is where the passenger needs to contact their travel insurer since this ( unless it is a pre-existing condition ) is something that insurance is for. If the passenger chose to self-insure , then that was their choice

In this situation, Emirates will waive the change fee ( as per fare rules ) but if there is a fare difference that is still applicable - this is also pretty standard for airlines

Without wishing to diminish the situation you found yourself in and with the greatest respect - VS (I assume it was Virgin Atlantic) is a much smaller airline than Emirates: carrying 5.8 million pax in 2013 compared to EKs 44.5 million. That's 120,000 passengers a day, and even with very low incidences of passengers with extenuating bereavement circumstances, say, 0.8% (global crude death rate), that's still 960 passengers a day. Without wishing to sound insensitive, you can see how to a organisation such as a big airline, it's not really that much of a rare event (for them) and for them to effectively ignore their revenue management models (aka, as flights become more full, they charge more money for the remaining seats - with added flexibility) is not insignificantly costly.

Your point about profiteering - I'm not sure whether airlines make enough money for it to be called profiteering: margins are thin. I know from our point of view, we are simply buying a seat on a plane and they are all the same, but from the point of view of the airline, they need to make x money from a cabin and adopt a progressive revenue model of selling their inventory so that more people can fly. I don't think many people who enjoy the modern world of relatively cheap air travel wants to go back to a system of flat fees all round :D

Out of interest, which airlines did offer special bereavement fares?

My experience with EK is totally different.

EK used to sell really cheap $99 AUD fares from Sydney to Auckland or Christchurch, over a 3 day period every January, so most of the upcoming year.

I used to buy them as my parents lived in Christchurch. I would then often get an upgrade offer for $100 which was a bonus.

So booked to fly Sunday morning, Mum dies Thursday evening.

Rang EK expecting to have to buy a new ticket.

Spoke to a very nice person in Mumbai, after 20 minutes I was rebooked on the first flight the next morning, and asked to produce proof of death before my return flight (which I stayed with my original return). The condition was that no proof my return flight would be cancelled.

I found this amazing service, and was happy to comply.

When I checked in the next morning, the airport manager was alerted and he came and spoke with me, showing compassion and concern.

However at the end of the day I will concede that EK is a business and needs to operate as such.

No one owes you anything, if you get good treatment, its a bonus.

Maybe it makes a difference how you treat the call centre staff when you want someting out of the ordinary

Lack of Compassion from Emirates - Very Poor
 

I think there is a huge difference between expecting a certain treatment in unusual circumstances that an airline isn't obliged to provide and basically a human being on the other side bending or twisting the rules because they are human. That for me is the key point, ifan airlines has certain rules so be it. If you encounter some compassionate treatment over and above the rules that is a person doing it because they want to not the airline. EK is so big now nobody can expect that exceptional treatment every time. Unfortunate but I think inevitable.

I strongly suspect that some of the problem here is in what OP is seeking. He wants to cancel his sister's ticket and rebook. Rather, what he should be doing is asking for an exception to make a change.

As others note, it is likely that the change fees and other fare rules will be waived on presentation of a death certificate, but the fare is the fare. I take it that the sister will be charged the lowest available fare for the date she wishes to travel. That might be the 350.

Hopefully OP's sister has travel insurance as this will generally cover the death of a close relative and would most often return her to the UK.