Liquidation is an auction, not a dump
Every epoch the ledger checks each position against its line. One that crosses it is auctioned: the price starts just above market and steps down each epoch until bids cover the debt. The rest of the collateral goes back to its owner, and bidders never learn whose it was.
Losses fall on lenders
If collateral sells for less than the debt, the shortfall is bad debt. It lowers the value of every share in the pool that lent the asset.
Private from the public
Positions are hidden from everyone watching the chain. The sequencer and replicas can read them, because they have to check them. Prices are posted by the sequencer, bounded by the pools.