Delta offers beravement fares. Call them and ask them if they can let you change/reschedue the flight (if not refund) due to the death in family. They may be able to do so. It all may depend on the agent you get through, and are they willing to escalate it to get it through for you or no.

https://www.delta.com/planning_reser...ment/index.jsp
(not directly applicable, but somewhat related showing that DL does offer something on this at least)