It’s an interesting thought but you gotta admit it would be silly to have a boss in a game that you absolutely cannot beat. Like your character just gives in to madness/despair as soon as you encounter the boss.
Now maybe if you had a dark souls boss fight while a different big unimaginable entity tries to catch up with you might be interesting. But that also might just be a countdown timer on the boss fight which could be lame if not done well.
Did you get a huge flood of emails at the start? That happened to me one time and it was because one of my old passwords got leaked. Buried within the flood of emails was a legit “your password has been changed” email for an account.