The Federal Reserve provides dollar swap lines to major central banks, such as the European Central Bank (ECB). The process works as follows:

1. The ECB allows European banks to give them US Treasuries at par value.
2. The ECB then provides dollars to these banks.
3. With the new dollars, the banks can handle any dollar deposit outflows.
4. The ECB obtains the dollars from the Federal Reserve using the swap line.
5. Throughout this process, no US Treasuries are actually sold.
6. Any negative profit and loss (PnL) resulting from the transactions are borne by the central bank, which can stomach infinite losses.
7. The dollar swap line balances increase, which will be reflected on the Federal Reserve's balance sheet.

This arrangement ensures that the financial system remains stable, and the banks can manage their dollar deposits without resorting to selling off US Treasuries.