Okay, so your node goes offline, the node you connected to can either publish the current receipt list to the global state, or it can publish an older version of the receipt list and if you don't come online to correct the record, the global state will accept the older version.
If both of you are offline, both of you lose access to the locked funds (assuming neither of you ever come back online), but the channel states of the other nodes you are connected to still got their respective payments.
You could prevent the other node to go rogue and try to steal your #sats by setting a #watchtower for your node.
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