If you know you are going to miss your outbound flight, I would call Delta and let them know. Explain the circumstances to the agent and, if you know when you can depart, ask them to see if they can find you seats on a flight that would work for you.

If you know you are going to miss the flight and have no idea when you will be able to go, you may end up returning the FF ticket to DL (re-depositing the miles to your account) and rebooking an award seat when you do know your travel dates.

disclaimer: I am not a Delta FF so there may be better solutions to this than I have offerred. Any DL FF'ers out there????

Good luck and I hope your relative feels better.