Called a 'bereavement fare' but may not be actually the cheapest available. Call airlines direct to get this sort of fare. Note they will need some details about the condition for travel.
For a good price I have found the rates at
http://www.worldwideflights.com/ or at:
http://www.wefly.co.uk/flightonly.html as just about the best on the web so if you need a cheap flight try the liinks.
I doubt the airlines fares will be athe above can offer though, and perhaps bear in mind that as you need to travel long haul, the absolute cheapest fare may not be the most suitable option in terms of type of flight, do you need an open return and even as basic as the comfort of the seat, etc...
I hope it works out ok for you...