This is open to interpretation, but this is how I see it.
Accept the blockchain history and do not try to retroactively modify it.
Nodes that try to change data in past blocks and recalculate the proof of work. Note:
To modify a past block, an attacker would have to redo the
proof-of-work of the block and all blocks after it and then catch up
with and surpass the work of the honest nodes. See Bitcoin Whitepaper pg. 3
The reason this is important is because, theoretically if more than half of the nodes on the network are trying to attack the blockchain, they might succeed and effectively gain control because collectively, they can compute the proof of work faster.
Does it make sense or what is interpretation of neither attacker nor
honest node succeed in finding a block ? What would that mean for the
consensus rule that there is a third side ?
I'm not sure what exactly you would define as a "third side", but if, for example, there was a third group that was not "honest" it would be considered another attacker. Now, if the third group is not attacking the blockchain in the same way as the other attacker group, that could split the chain into 3 different forks: 1 "honest" chain, and 2 different "compromised" chains.