Question: I have a large ceramic soup cup which appears to be internally damaged after being rinsed with cold water while hot:

![Ceramic cup with visible cracks throughout](https://i.stack.imgur.com/kj0v8.jpg)

Is this cup still safe to use, or is it likely to shatter or otherwise fail during use?

Answer: 
That is called crazing. It is a crack or fissure in the enamel coating on the cup, not indicative of deep structural flaws.

Your cup is unlikely to fail in the sense of completely breaking due to the craze in the glaze.

On the other hand, they will stain over time, and be unsightly, and hard to wash out. 

If the piece is old enough, the glaze may contain lead, which can leach due to the crazing. In that case, the piece should definitely be discarded.

Technically, most health codes require crazed dishware to be discarded, although you can assess your tolerance for risk.
As anybody who has ever made something from ceramic and has tried to paint it knows, ceramic is a very porous material, which will soak up some of whatever touches it's surface. That is the very reason why a glazing is needed to seal it, in order to make it food safe, if we want to make something, such as a cup, from it. If that ceramic cup were to be left unglazed, it would soak up some of whatever is put into it and we would never be able to clean it all out. Whatever is soaked into the ceramic, would then grow mold, trap bacteria and so become a health hazard. 
That is the reason why most health codes require any ceramics used to serve food or drink, to people, to discard crazed ceramics. The crazing (cracks in the glass sealing the ceramic) in a cup, does not give us cause for concern that the cup might break and spill hot liquid onto a person, because that will not happen, due to crazing alone. Crazing is simply cracks in the glazing that seals the ceramic beneath it, thus rendering it a health hazard to anybody drinking from it. 
We should be careful to never discount a health code, as rediculous, simply because we may not understand the reason(s) behind it. Those rules haven't been arbitrarily thought up to create a hassle, or hardship, for people serving food. They have been created to protect us, for a verifiable reason, from a danger to our health.