Earlier quoted context omitted.
Calling the case of the network halting "safety" doesn't help things. To walk through a plausible example: let's say 3 Chinese services control 35% of the stake of Algorand. Without warning or any public announcement, the Chinese government steps in and forces them to turn off their servers. The Algorand network will now stop functioning as it can't reach 2/3rds. Hours go by and no one is able to transact. At this po…
In this case the Chinese government can kill the liveness of the network (preventing it from producing new blocks), but not the safety of the network (they can't fork the chain). Your question has changed into: "doesn't the system break when a malicious party controls 35% of the stake?" To which the answer is yes. If a malicious party can control 35% of the stake, that is very bad. I should add, though, that if you k…
That didn't happen in this case. The Chinese government never took anyone's keys or controlled any stake, which is the point of the example.
The malicious parties don't need control. They don't need to take anyone's keys or access their servers. They just need to be able to bring it offline, which is much easier to do.
Which raises the question I asked and you didn't answer: if 35% of the stake goes offline with no signs of coming back, how do participants reach consensus?