How would they or anyone else know that their last words were their last words? Why would anyone else know they should remember those words?
I knew the last words of one of the people I roomed with in the hospital 5 years ago. I was the last person she spoke to, as it was about 4 am, I'd been up to use the bathroom, she was awake and in the mood to chat for a few minutes. We talked a bit, and she was mentioning some of the nurses she didn't like. Well, there were a couple I didn't like, so we agreed to have a gossip session later on that morning.
We never had that. She died maybe an hour or two later, in her sleep. The nurses who came on-shift at 8 am found her. Her family came... and of course in situations like these, the roommate isn't supposed to be involved. I got hustled, bed and all, down to a lounge that had been converted as overflow space for patients (the hospital was, as usual, over-capacity). I never had a chance to tell them what her last words had been, that she'd been in an alert state of mind, or anything else.