What is the solution for distributed append-only storage?

Question

Database

Some time ago I was at a conference about blockchain. On it, an unknown person from the audience suggested that the technology of secure (from changes) distributed databases in an untrusted environment has long been solved. The person left in English, and now I am looking for any information about such systems.
Let's formulate the points:

• Append-only data without the possibility of change (or the fact will become known to everyone and can be ignored)
  
• Data is stored distributed up to several thousand participants over the Internet
  
• Network participants have the ability to unauthorizedly change the logic of their node (scammers)
  
• The system must be stable (within reason) to the failure of a part of the nodes
  
• This is not a blockchain
  

Answer 1

Technically, it's possible.
The existence of such a stable system with thousands of participants is doubtful.
Why do these thousands need it.