Every year, hundreds of departing employees at Bloomberg L.P. are presented with a choice: Either leave the company empty-handed or accept a generous financial package and agree to never speak ill of the company. Many take the money.

The result is that some employees at Michael R. Bloomberg’s company are barred from publicly describing misconduct and what they perceived as an entrenched culture of bullying, where women are often objectified and sometimes face discrimination, according to interviews with more than a dozen former employees, as well as lawsuits and internal corporate documents reviewed by The New York Times.

Bloomberg is not unique. In corporate America, in order to receive severance payments, fired or laid-off employees generally must sign agreements that require them to keep quiet about their experiences. Such agreements are deployed for a range of reasons, including to protect intellectual property, to prevent departing employees from publicly vilifying the company and to confidentially settle claims of discrimination or harassment.

But unlike just about every other company in America, Bloomberg’s owner and founder is running for president.

The heavy use of so-called nondisclosure and nondisparagement agreements at Mr. Bloomberg’s company has gone from being a standard business practice to being a political vulnerability on the presidential campaign trail.

Mr. Bloomberg’s Democratic rivals have accused him of using his multibillion-dollar fortune to silence victims of abuse and discrimination. In response to the criticism, Mr. Bloomberg recently released three women from nondisclosure agreements who he said had complained about comments he made. And he said that as long as he was running the company, it would stop using nondisclosure agreements with employees who have sexual harassment or misconduct claims.

“I recognize that NDAs, particularly when they are used in the context of sexual harassment and sexual assault, promote a culture of silence in the workplace and contribute to a culture of women not feeling safe or supported,” Mr. Bloomberg said in a statement.

But that change only affects a small fraction of the nondisclosure agreements that are put in place on a regular basis at Bloomberg. Most people who sign do not have specific claims of mistreatment; instead, the contracts are designed to prevent disgruntled ex-employees from bad-mouthing their former employer.

Natalie Harland, a Bloomberg spokeswoman, defended the company’s culture and practices.

“Bullying and discrimination are not tolerated,” she said, noting that Bloomberg consistently ranks at the top of employee satisfaction surveys and provides six months of paid parental leave.

“Mike has worked to create an environment where women can — and do — succeed,” Ms. Harland added. “The company provides competitive pay, good benefits and opportunities for advancement.”

Mr. Bloomberg’s company makes the bulk of its money selling a proprietary financial data system to Wall Street firms and other major companies. Every new hire has to sign a confidentiality agreement, which requires that they not share trade secrets and refrain from poaching anyone from the company after they leave, usually for a period of three years.

Employees who are fired or resign in frustration are often pushed to sign contracts that prohibit them from in any way disparaging the company, several of the former employees said in interviews. Those pacts bar the employees from even acknowledging the existence of the agreements, according to contracts reviewed by The Times.

Bloomberg’s contracts are in line with those used by other major companies, independent employment lawyers say. In some circumstances, The Times also requires employees to sign nondisclosure agreements in order to receive severance packages.

“I don’t know of a company that provides severance that doesn’t ask for those people who are subject to that severance to sign a nondisclosure agreement,” said Melinda Wolfe, who was the head of human resources for Bloomberg from 2008 to 2013.

The Times spoke to 13 former Bloomberg employees — including some who now work for The Times — who said they wanted to be released from their exit agreements so that they could speak openly about the culture at the company now that its founder and owner was running for president. If they were free to talk, some of the former employees said, they would describe a company that, while it provides generous pay and benefits, can be an uncomfortable place to work, especially for women.

Some Bloomberg managers perceived the use of medical or maternity leave as stealing from the company, several of the former employees said. One, Andreea Orent, said she was chastised for being a few minutes late to work and had been called out in a performance review for once clocking in 20 minutes late. Ms. Orent is suing the company for discrimination.

Ms. Harland, the Bloomberg spokeswoman, said the company didn’t fire Ms. Orent, even though she “was frequently late for — or would miss altogether — important meetings.”

Men at the company rated the “hotness” of their female colleagues, according to an interview with a former employee and lawsuits against the company in 2016 and 2018. Employees said in lawsuits that women were encouraged to wear short skirts and high heels.

Ms. Harland said the company had not found evidence of men rating women based on attractiveness and that there is no dress code at Bloomberg. She said that when the company discovered one instance in which men at the company “started a chat that included inappropriate comments” about women, Bloomberg fired the employees involved.

Mr. Bloomberg has a history of making derogatory comments toward women, including at his company. At a business meeting in 1999, he said that if he let women who had children have flexible work arrangements, he would have to give men time off to work on their golf games, according to an employee who heard the remark and is now bound by a confidentiality agreement.

“If women wanted to be appreciated for their brains, they’d go to the library instead of to Bloomingdale’s,” Mr. Bloomberg was quoted as saying in a booklet compiled by his former chief marketing officer.

Ms. Harland said Mr. Bloomberg “openly admits that his words have not always aligned with his values and the way he has led his life, and some of what he has said is disrespectful and wrong.”

Some employees, who believed that they had legal claims against the company, said their lawyers or colleagues advised them to accept financial settlements rather than mount a yearslong battle against a company with virtually unlimited resources.

One woman said she had signed a nondisclosure agreement after accusing Bloomberg of firing her after she complained that she was passed over for promotions when she returned from maternity leave. The Bloomberg spokeswoman said the woman lost her job as part of a restructuring. A black sales manager said in a confidential complaint with the Equal Employment Opportunity Commission, which the Times reviewed, that she had been paid less than her white colleagues and had been fired for complaining to human resources. She later signed a nondisclosure agreement as part of a settlement with Bloomberg, according to a person familiar with the matter.

Others had more run-of-the-mill grievances about the company’s culture and how they were treated — the type of issues that they were willing to swallow in exchange for money.

Laurie Hays, a former top Bloomberg News editor, was personally fired by Mr. Bloomberg five years ago in a glass-walled room in a bustling newsroom, in what many employees viewed as a deliberate act of public humiliation. She signed a nondisclosure and nondisparagement agreement.

Ms. Hays, who now works in public relations, said she “loved every minute” of her time working with journalists at Bloomberg. Ms. Harland said Mr. Bloomberg had not intended to humiliate Ms. Hays.

Two of the company’s other top female editors, Ellen Pollock and Megan Murphy, also were pushed out after Mr. Bloomberg returned from his time as New York City mayor to run the company. Like Ms. Hays, Ms. Murphy signed an agreement to keep quiet.

It is not clear whether Ms. Pollock, who is now The Times’s business editor, signed one. She said she had not discussed the details of her departure with anyone other than her family and lawyers.

Several former employees said in interviews and court filings that they felt pressured to forfeit the right to speak out.

A marketing employee said human resources had told her that if she didn’t sign a nondisclosure pact, Bloomberg would charge her for the thousands of dollars it had spent sponsoring her green card. She signed.

In another case, Bloomberg demanded that a person who didn’t even work for the company — Leta Hong Fincher, the wife of a departing Bloomberg reporter — sign a nondisclosure agreement. The company threatened to sue her and force her to repay the tens of thousands of dollars it had spent to move the couple from Beijing to Hong Kong. Ms. Fincher never signed the agreement; Bloomberg didn’t sue. Her husband, Michael Forsythe, is now a reporter at The Times.

Ms. Harland said that Mr. Forsythe “stole Bloomberg L.P. intellectual property and gave it to his wife” and the company was seeking to protect the information. She added that Bloomberg did not pressure anyone to sign nondisclosure agreements.

Laurie Evans worked in sales for Bloomberg’s Businessweek magazine. In 2016, she was hospitalized after suffering a severe panic attack at work. While she was medicated, a Bloomberg human resources employee called her to say she had been fired and needed to sign a nondisclosure agreement if she wanted to receive severance, according to a legal complaint.

Ms. Evans signed. She received part of her salary plus about $70,000 in other cash payments. In exchange, she agreed to “not, in any way, disparage” the company or say anything to anyone “that may be considered to be derogatory or detrimental to the good name or business reputation” of Bloomberg, according to a copy of her agreement.

Ms. Evans later filed a lawsuit in which she claimed that she had been coerced into signing the agreement at a time when she was in intense psychological distress. Bloomberg has argued in court that Ms. Evans’s claims have no merit and she was mentally competent at the time. The suit, in a New York court, is pending.