When Reza Zarrab, a gold trader based in Turkey, was arrested on a recent trip to the United States and sent to New York to face federal charges, his lawyer tried to keep him out of prison by tapping into Mr. Zarrab’s considerable wealth.

His client would post a $50 million bond, secured by $10 million in cash. He would stay in a rental apartment in Manhattan and wear a GPS monitoring device. And one more thing: Mr. Zarrab would pay for 24-hour guards to ensure that he did not flee and to escort him to and from the courthouse.

The request, which a judge is expected to take up on Thursday, is not as unusual as it may seem. The rich are different from everyone else, even those accused of crimes. But a handful of extremely wealthy defendants, particularly those from overseas, are testing courts by proposing to live in self-financed gilded cages while they await their fate.

Prosecutors vigorously objected to Mr. Zarrab’s being allowed to face trial under such conditions, telling a federal judge in Manhattan that the proposed plan would allow a rich defendant to build “a personal jail for himself” in a Manhattan apartment, “staffed by a firm on his payroll.”