Empty offices and unanswered messages have compounded the confusion over the new law, which is called the First Step Act, as thousands of inmates, and their families, seek information about whether they will be set free.

In addition to creating a system that will allow some low-risk inmates to earn early release, the new law also retroactively increases the number of days inmates receive off their sentences for good behavior. Inmates now get 54 days for each year of their sentence, up from 47, a retroactive change that could potentially free as many as 4,000 inmates, according to The Marshall Project, a nonprofit news website covering the criminal justice system.

Amadi Busiris, 50, who is serving out the tail end of a 30-year sentence for conspiracy to distribute drugs, had been closely following news reports about the bill’s progress from his prison cell, and then more recently from a halfway house in Washington, D.C., where he has been sent to await his release in November.

After the law’s passage, Mr. Busiris believed that he would be able to walk free almost immediately. But when he called his lawyer to start the process, he was told that he would have to wait until after the shutdown, he said.

“The law passed but they are not making any moves,” he said, adding that seven others in Hope Village, the halfway house where he lives, are in the same situation. “We are just stuck.”