Say there is one large company that consists of many smaller companies. The former is 100% shareholder of the latter, so there is no doubt about who owns what.
One of those smaller companies exists and is registered as such in a different country.
Can the owning company be prosecuted in its country for something the smaller company does (of its own accord or as instructed to by the owning company) inside the other country? For the sake of argument, I'm not talking about murder or anything grotesque, but rather an illegal activity in the sense of civil laws about e.g. software use and intellectual property and/or copyright, which often differ subtly between countries across the world. No products or anything else containing anything "illegal" is transferred to the owning company's country (which would be obviously prosecutable).