Yesterday evening, having heard nothing one way or another, I tried calling Mom. To my great relief, she answered her phone and announced that "rumors of my death have been greatly exaggerated." What appears to have happened is that someone up in the hills with a similar first name to my mother died, and when it passed through a game of "Whispers" it had gotten turned into my mother dying instead.
Now the call cut off in the middle, but that's not uncommon. They have bad cell reception and Mom isn't great about remembering to keep her phone charged. However, Mom is not only alive, but said she was feeling pretty good, and was in the process of cleaning and polishing the large amount of wood in the house in which she's living these days. Before the call dropped, she also said that she's spoken to my sister, so there's an end to the panic.
This afternoon, I got texts from the family friend who had frightened Kelli (and by extension me) apologizing for the mistake.