It really depends on the consensus algorithm being used on your private chain. For Quorum related information, I would suggest reading their RAFT documentation. You could also read about QuorumChain (although this has been deprecated)
For private chains, and non mainnet chains you'll need to take a look at the consensus method being used. The two Proof of Authority consensus alrogithms I can think of off the top of my head are Clique, and Aura. I wouldn't go so far as to say that Quorum and private chains have single points of failure, Blockchain's, irregardless of their consensus methods are designed for high availability, no SPOFs, etc.. What they do have, generally, are centralized consensus methods.