If you design and sell tshirts globally on the internet or freelance copy edit for clients in and out of country or exhibit and sell your art internationally these are all sorts of things that are not in competition with local employment but currently have limited movement and residency options. They're not pure examples but I think they work for what people are typically concerned with when it comes to immigration and residency.

Being wealthy or just having enough in savings to not have to work for a while seems the obvious alternative.