I keep hearing "you can't do X without getting slashed". What happens if there is a network partition that lasts for longer than 6 minutes? Which two of the diverging blockchains get to slash the other one and take all their stake?

> What happens if there is a network partition that lasts for longer than 6 minutes?

With less than 2/3 of the total stake active on a single partition, that partition stops finalizing transactions, meaning that the chain explicitly stops guaranteeing that it's canonical.

Notably, slashing cannot result from a partition, only from malicious validator behavior.

> Which two of the diverging blockchains get to slash the other one and take all their stake?

For a partition, which is not a slashable offense, there is no slashing. The minority partition stakers suffer inactivity leak on the majority chain, meaning that they very slowly (at first) start losing their stake until the majority partition has 2/3 stake again. It's not a big penalty like slashing, unless the chain remains in a degenerate state for many hours or days.

On the other hand, a slashing rules offender (attacker) gets slashed on all chain forks. The conflicting signed block from one gets included on all others for a bounty. This means that every staker must vote for only one fork at a time, which means the network can eventually determine which fork is canonical because it was voted for the most.