This basically is about the legal responsibility a web-site owner has for user-created content that violate copyright or other laws (such as libel laws).
In the USA, this situation is covered by the DMCA. In the EU, this situation is covered by the e-commerce directive. In other jurisdictions, other regulation may apply.
The DMCA (USA) is the simplest of those regulations. It stipulates a protocol of Notice and takedown. A web-site owner that complies with this protocol is given Save Harbour. This means that a compliant web-site owner cannot be sued. This goes both for a web-site that is a registered business, and a site run by an individual.
The owner of the IP may, however, take the individual who stole and published copyright protected work to court, and will do probably do so if the financial loss was substantial (e.g. a major motion picture was leaked before hitting the cinemas).
In the EU, the law is much less explicit than in the USA. Basically, the Notice and takedown protocol works like in the USA, but since it is not part of the law, it is less formal. In the USA, you can safely not act on any complaint that does not strictly follow the protocol (you just have to give feedback so they can fix it). Not so in the EU. And as follows from Delfi AS vs. Estonia, you can be sued even if you take down stuff. In particular if you create an environment for anonymous postings that encourage transgressions and have no means of moderation in place.
So if the web-site is located in the EU, the website owner need to exercise more caution when he lets friends publish content, than when a website owner in the USA.