That is much easier than you might imagine.
However I understand that most of the unlawful stuff is done in some place like Germany or the US, but all access to the site is via proxies in remote parts of the world which use a VPN to talk to the main server.
For an example that won't get you sent to jail just for asking: Google (or better yet Duck Duck GO) the term FOSI and follow the link to the site. FOSI has been offering downloads of unlawfully copied software since at least 1990 (when I first found them). They have never been down for more than an hour despite all the DMCA fuss!
Setting up an unlawful site is not hard, but your DO need someone competent that you can trust to set things up - it is the dumb mistakes that kill you!
I think you mean illegal. There is no such thing as an "unlawful" copyright violation because copyright is a creation of statute not of natural right. Copyright doesn't even exist at common law. In fact copyright didn't even really exist till the player piano was invented.
I used copyright as an example so I could illustrate my point without anyone going to jail. Yes there are gambling, child porn, drug dealing etc. sites that have been around just as long, but you risk jail time for even looking.