The closest analogy I can think of is legal trusts, that have a stated purpose with little room for interpretation, but still has a human performing the operations.
Darknet markets take bitcoin, and at least some VPS providers do as well, so no need to get "real" bank accounts and evade know-your-customer.
You can hire humans for things over informal channels with no intermediary, but what do you do for reputation/accountability when said humans need to keep low enough volume to not interest the tax authorities?
I guess algorithmic trading on decentralized/anonymous bitcoin markets is one way to have no humans, if you can get the volatility low enough.
How do you exploit capital with (almost) no human involvement?
Imagine a trading bot that hires people to improve it's source code, and other people to oversee those people, but there's nobody in charge - i.e. nobody to tell the bot to stop doing what it's doing.
Automated trading is another. Selling advertising is another.
Perhaps it could make and sell artworks.
However it's not theoretically impossible. Plenty of services are done over the internet with no human interaction.
Also, nobody says that such a bot wouldn't be profitable. It could send dividends to the creator (or do something else worthwhile with the money - a'la trust funds), it's just that the creator wouldn't be able to modify or stop it any more.