My wife passed away (unexpectedly) last February. I had to cancel 5-6 planned itins with DL in the days/weeks after. I have to say DL couldn't have handled it better IMO. The first call I made was on our 2nd of 3 ER visits preceding her death. As others said, they asked for the hospital info, but I just gave them the main phone number, and to my knowledge they never called. The day she passed, they didn't ask for anything as I cancelled the next two weeks of trips. I called at least once more to cancel another trip, and they still didn't ask for anything. That's one of the reasons I love DL.
The flip side of that coin was Wells Fargo (Dealer Services), who by far had the worst customer service of any company I've ever dealt with (needed them to re-title a joint auto we had). As a result I closed all our WF accounts, paid off the car and I will never do business with WF (or any of it's shell companies) again.