I think you should make the overwhelmingly likely case crash in a controlled way, but provide a way to handle it for people who truly want to keep going in such strange conditions.

In rust I would panic in now(), but also provide a alternative call that returns a result named something like try_now(), similar to Vec::with_capacity and Vec::try_with_capacity.
In languages that provide them, you could also throw a runtime exception that can be ignored and just bubbles up to main unless explicitly caught.