NEW ORLEANS — The judge told Johnny Traweek he had served his time, seven months, for hitting someone with a saucepan in a drunken fight, then suggested he could be released from the Orleans Parish prison by midnight.

Mr. Traweek began giving away his jailhouse comforts — a blanket, two orange sweatshirts, ramen, soda. Then he waited out the final hours of May 2, 2018, his last legal day behind bars.

Midnight came, midnight went. Around 4 a.m., Mr. Traweek was lying in bed, eyes open, when the staff summoned inmates for predawn breakfast. He would repeat that routine, including the sleepless nights, 19 more days because the Louisiana Department of Public Safety and Corrections did not process his paperwork in a timely manner.

“It’s a bad, bad feeling,” said Mr. Traweek, now 70. “Every day, I’m getting up and thinking I’m going to get out. And it doesn’t happen. I knew I wasn’t in there for any charge, and still I have to sit there.”

Mr. Traweek’s case was neither atypical nor the worst of its kind: Roughly 200 inmates are held beyond their legal release dates on any given month in Louisiana, amounting to 2,000 to 2,500 of the 12,000 to 16,000 prisoners freed each year. The average length of additional time was around 44 days in 2019, according to internal state corrections data obtained by lawyers for inmates — and until recently, the department’s public hotline warned families that the wait could be as long as 90 days.

In most other states and cities, prisoners and parolees marked for immediate release are typically processed within hours — not days — although those times can vary, particularly if officials must make arrangements required to release registered sex offenders. But in Louisiana, the problem known as “overdetention” is endemic, often occurring without explanation, apology or compensation — an overlooked crisis in a state that imprisons a higher percentage of its residents than any other in most years.

The practice is also wasteful. It costs Louisiana taxpayers about $2.8 million a year in housing costs alone, according to department estimates.

“The state has not made liberty, or taxpayer money, a priority in how they run their prisons,” said William B. Most, a lawyer based in New Orleans who has filed two class-action lawsuits on behalf of overdetained inmates.

“To our clients, it is an extremely scary experience because they do not know why they are being held, when they will be free or how they can get free,” he added. “All they know is they should not be behind bars.”

In December 2020, the Justice Department opened an investigation into the practices the state used to determine the release of its prisoners, particularly those, like Mr. Traweek, who remained behind bars despite being eligible for immediate release. The investigation, according to people with knowledge of the situation, is expected to find widespread violations of a federal law that guarantees imprisoned people their “rights, privileges or immunities.”

State officials have been cooperating with the investigation, so it is possible it could result in an agreement. Such a deal would probably require an overhaul of procedures used to calculate time served, according to people who have spoken to investigators, and mandate the replacement of the state’s outdated corrections computer system known as CAJUN. (Its error message is a pixelated pop-up of a bunny behind bars.)

Prisoners’ rights groups say that federally mandated changes, while welcome, would do little to overcome the core problem that defines Louisiana’s troubled criminal justice system: an entrenched belief that an inmate’s freedom is worth less than everyone else’s.

“We exist in a space between malice and incompetence,” said Jamila Johnson of the Promise of Justice Initiative, a nonprofit in New Orleans that has sued the state for unlawful detention and poor treatment of prisoners.

A spokesman for Louisiana’s corrections department declined to discuss overdetention or even provide basic information about how the system operates and declined to respond to specific claims by inmates, citing the continuing litigation.

But in a deposition taken in January, James M. Le Blanc, who has run the agency for 14 years, acknowledged that the state has “had a problem with immediate releases” since at least 2012. He said the department had halved waiting times in recent years, from an average of more than 70 days a decade ago, and claimed that parish prison officials were also responsible for the drawn-out releases.

“We’re not where we need to be,” he added.

The problem crops up sporadically in other states, including neighboring Mississippi, and in the federal Bureau of Prisons. New York City recently agreed to pay out as much as $300 million to thousands of current and former inmates at local jails who had been kept hours or a few days after they were supposed to be released. But those waiting times are relatively short compared with what prisoners in Louisiana endure.

The state routinely sends prisoners with sentences under 20 years (and those with serious physical or mental conditions) to jails or prisons run by governments in local parishes, which are the equivalent of county governments elsewhere. That means parish prisons serve not only as traditional jails, but also as officially designated extensions of the state prison system.

It is a jumbled and sluggish system with tangled lines of communication and jurisdiction — and many of the prisoners who have been kept past their release dates fell into the chasm between dysfunctional state and parish bureaucracies.

A judge freed Brian Humphrey from the jail in Bossier Parish in northwest Louisiana on April 16, 2019, after he had served three years for an offense related to assault. He prepared to leave that night. Instead, he languished.

The corrections department, for reasons that remain unclear, waited 10 days to even begin processing his paperwork, according to records obtained in a 2021 class-action lawsuit his lawyers filed against the state. Instead of freeing Mr. Humphrey, as he was legally bound to do, the parish sheriff transferred him to a state-run work camp outside Shreveport, where he stayed until he was released on May 13, 2019.

That was 27 days beyond his release date.

Louisiana has one of the most overcrowded prison systems in the country, yet parish sheriffs are often reluctant to release people they believe are at high risk of committing new crimes. Some even view inmates housed in local facilities as worth holding onto as free labor.

In October 2017, Sheriff Steve Prator of Caddo Parish, which includes Shreveport, told reporters he was concerned that a recent criminal justice effort in the state was bad for parish governments. Not only would it result in higher crime rates among the “bad” former prisoners, but it would also deprive his staff of free labor provided by the “good ones.”

“They’re releasing some good ones that we use every day to wash cars, to change oil in our cars, to cook in the kitchen, to do all that, where we save money,” Sheriff Prator said.

There are few incentives for rushing an inmate out the door, especially if the state is picking up the tab: Reimbursement rates for state prisoners are a significant source of income in the parishes, and a handful of parish facilities have eagerly accepted migrants detained at the border, which offers even higher federal reimbursement rates.

Even well-intentioned corrections officials must navigate the state’s complex web of sentencing statutes and time calculation rules before signing off on the release of a prisoner.

Over the past several decades, formulas for sentencing guidelines have shifted, and record keeping has been spotty. Those documents can span multiple decades and cover several facilities, making it hard to nail down a precise accounting of time served — which is often the cause of snags.

Sarah O’Brien, a supervising lawyer with the public defenders’ office in Orleans Parish, has tried to take a more proactive approach. She reviews court records for prisoners around the state, typically those serving longer sentences, who might be entitled to immediate release because of errors in their time calculations.

She is constantly consulting a photograph on her phone. A cheat sheet she put together, written in fastidious longhand, lists all the relevant state laws and their dates of passage. It covers a full page of graph paper.

She also cultivates relationships with court and corrections workers. Recently, she moved up an inmate’s release date by a year after tracking down a juvenile detention record believed to have been lost in the flooding after Hurricane Katrina in 2005.

Ms. O’Brien found a back-office worker who had access the paperwork, and the woman responded, “If there are records, I got ’em!”

She found them, and the man was freed.

Just as often, the opposite is true, lawyers and inmates say. Officials in the system can hold up a release on little more than a whim, sometimes because they have interpreted a judge’s decision in their own way.

One former inmate from New Orleans served more than 18 months beyond his three-year plea agreement because a staff member in his state-run prison in Homer, La., noticed a glitch in the document signed by his trial judge — the order the charges were listed in was incorrect — that should have had no bearing on his release.

The prisoner, a man in his late 40s who spoke on the condition of anonymity because he was incarcerated for a sexual offense, wrote letter after letter to state officials. After a few months, he had what he assumed to be a breakthrough. The prison official who had blocked his release promised she would personally walk him out of prison if he was able to retrieve a missing document from the court.

It took him weeks to do so. When he turned it over, he instead waited for months before his case was finally sorted out.

He withdrew from the inmates he had befriended, fearful that his growing anger would spill over into physical aggression, and threw himself into his job as an orderly, sweeping up his cellblock and collecting garbage. Only during weekly Bible study sessions would he engage.

“How do I describe what it’s like?” he said. “It’s like you’re pretty much a nobody. You can write. You can request to speak to this person or to that person. But you’re at their mercy — why? — because they don’t want to be bothered.”