There's an old folk belief, still passed on in a "boogeyman's going to get you" sort of way, that if you sleep with your belly button exposed the thunder god, Raijin, will eat it. And probably the rest of you in the process.
This probably came from the older belief that Raiju, the god's pet, is a shapeshifter that would curl up in a convenient belly button to sleep.
The end though, I think that's connected to the author's other work that suggests that as cute as the Yakumo family is, there's a darker layer deep down, where Yukari is grooming and altering Ran little by little to become her replacement. Read Golden Cutting Line for more on that theme.