If someone's interested, I think the closest thing would be na LLC with bearer shares, but the issuance and use of them have been banned or heavily restricted in many countries over the years. An expert should be consulted to assess whether having bearer shares is worth the trouble.
Yes, AFAIK this is still legal even in some countries in Europe (it was in fact discontinued this year in one of the biggest tax havens Netherlands) BUT under new AMLD5 laws are heavily frowned upon and will likely anyway get you in trouble down the line. Basically, the latest edition of the AML directive means that anything that is against the spirit of the law -- even if it's not against the letter of the law -- will be deemed equally wrong. So, while tax avoidance is strictly speaking not illegal, it can result in public exposure, which, is about as damaging as actual tax evasion, just without the fines -- though a dozen EU states have recently rejected that.
The only country left that issues the type of anonymous bearer shares OP is looking for is Marshall Islands. Now you know why they're blacklisted by OECD, and so it's also pointless for you to go down this road, as you're painting a bull's eye on your back if you register in MI.
There's also Panama, but you have to pay a hefty bank fee for holding them (so pointless anyway).
