So, on a micro-level, let's say I have a function that expects x to be a float between 0 and 1, and there's some math and logic built on this assumption. Of course, in development if this expectation is violated, we fail fast and loudly and then fix the problem. In production it's not quite so clear. But still, is it ever the right thing to ignore that an invariant is violated and just hope that things somehow work out?

> Make defects obvious during development so they don't exist when you deploy to customers.

I agree with this phrasing. From another viewpoint, I would say:

If your code checks an invariant, and that invariant is broken never (never!, not even in production) just continue on and hope that things will work out.