Under pressure from federal authorities, the Swiss bank UBS is closing the hidden offshore accounts of its well-heeled American clients, potentially allowing their secrets to spill into the open.

In a step that would have once been unthinkable in the rarefied world of Swiss banking, UBS will shut about 19,000 accounts that prosecutors suspect have gone undeclared to the Internal Revenue Service.

UBS will transfer the assets to other banks or other divisions within UBS, or will mail checks directly to the account holders, creating paper trails for federal prosecutors who are examining whether UBS clients used such accounts to evade taxes.

The clients now face stark choices: they can cash their checks, and thereby alert the authorities to any potential wrongdoing, or not cash them, effectively losing their money.