How the heck should a library author know whether an error is recoverable or not? In many situations that depends entirely on the caller. Not-so-contrived exam

How the heck should a library author know whether an error is recoverable or not? In many situations that depends entirely on the caller. Not-so-contrived example: a config options contains a value that leads to a division by zero in some library I'm using. I don't want that to crash my whole program, I want to tell the user "hey this part didn't work" but be able to continue with the other parts. Without writing a ton of boilerplate code.