Apple secretly linked my account to my >15 year old inactive account as well as another random account that isn't even mine. Nothing happened of it until I let my iPhone sync its settings to a new iPad. The iPad spammed a password input form for my old account that blocked all other UI elements. It didn't accept any password even after a password reset. Took me an hour to make the tablet usable again. The password form still randomly pops up every few weeks and there seems to be no way to fix the mess.
Bonus: the iPad's device name is now "My iPhone" because it also synced the device name from the phone.
I had this same issue. About once a week it would prompt me for the password for an old Apple ID. I eventually started over from scratch to work around the issue.