Two decades after Arthur Andersen LLP’s downfall, the firm that audited Enron Corp.’s financial statements remains a punchline for many, though some prefer to remember it as an influential institution deserving of respect.

The accounting firm stopped auditing public companies on Aug. 31, 2002, and wound down its operations. Its demise turned the Big Five into the Big Four: Deloitte Touche Tohmatsu Ltd., Ernst & Young LLP, KPMG LLP and PricewaterhouseCoopers LLP.

For many of the thousands of auditors who worked at Arthur Andersen, in particular, its collapse remains a painful reminder of how fragile livelihoods—and even a company’s existence—can be.

Founded by accounting professor Arthur E. Andersen in 1913, the firm was based in Chicago. At its peak, Arthur Andersen employed about 85,000 people in 84 countries. Thousands of them found jobs in professional services, largely at the Big Four.

The firm, which reported roughly $9 billion in global revenue for fiscal 2001, was in 2002 convicted by a Houston jury of obstructing the government’s investigation into Enron by shredding thousands of records and deleting tens of thousands of email messages, impeding an investigation by the Securities and Exchange Commission.

Enron, a Houston-based energy company that had been an Arthur Andersen client for 16 years, hid hundreds of millions of dollars in losses and similar amounts of debt through transactions involving some of its senior officials.

The Supreme Court in 2005 unanimously overturned Arthur Andersen’s criminal conviction, concluding the judge’s instructions to the jury were flawed and making it clear that lawyers and executives have some latitude in destroying sensitive or outdated documents.

Shredded Enron documents remain the subject of internet memes and jokes.

Earlier this year, a Reddit user shared an animated image of documents falling from a printer into a paper shredder, with the caption “Live from Arthur Andersen.” Rutland Price, an accounting analyst at financial-services firm Protective Life Insurance Co., responded to the shredder image by pointing to the Supreme Court ruling, which came too late to save the firm. “You get a lot of Arthur Andersen memes that I don’t think are quite justified,” Mr. Price said.

Accountants still joke about Arthur Andersen. When the SEC in June announced its $100 million fine against Ernst & Young for exam cheating, Jacob Jellison, a tax accountant at professional-services firm Moss Adams LLP, quipped that EY employees must feel lucky they’re not working for Arthur Andersen because of what happened to the firm. The colleague sitting next to him in the lunch room laughed.

Arthur Andersen, Mr. Jellison said, serves as a reminder that “no one is too big to fail.”

Former Arthur Andersen employees have ascended to top perches at consulting, auditing and tax firms and include current or former chief executives at professional-services firm Grant Thornton LLP and consulting firms Alvarez & Marsal Holdings LLC, Protiviti Inc. and West Monroe Partners LLC.

Having an Arthur Andersen background makes many of them better auditors today, according to a study by academics from five universities that was published earlier this year. The researchers compared audits conducted between 2016 and 2019 by roughly 200 Arthur Andersen alumni to audits by nearly 1,500 of their peers at Big Four firms who hadn’t worked there. They found that Arthur Andersen alumni provided higher-quality audits, with fewer restatements or signs of potential earnings manipulation in the financial statements.

After Arthur Andersen’s demise, Congress passed the Sarbanes-Oxley Act to overhaul U.S. financial reporting and corporate governance practices. Audit quality has improved since 2002, but certain areas, such as auditor independence, are still lacking, SEC Chairman Gary Gensler said last month.

The Andersen name has survived in the form of an association of consulting firms offering tax and legal services. Former Arthur Andersen partners bought the rights to the name in 2014. The association, now called Andersen Global, employs more than 12,000 people.

“The trust in the brand is absolutely critical,” said Rohit Deshpande, a marketing professor at Harvard Business School. “It’s unclear to a lot of people whether Arthur Andersen was the principal bad actor or whether it was collateral brand damage from Enron.”

Joseph Berardino, who led Arthur Andersen until March 2002 and is now a managing director at Alvarez & Marsal, and David Duncan, the lead partner on the Enron audit, didn’t respond to requests for comment.

Some former Arthur Andersen employees are memorializing their treasured experiences at the firm. Warren Turner, a former audit manager, is working on a book about the firm slated to be published this fall. Mr. Turner and six other alumni have collected interviews from more than 4,000 former employees, he said.

“I think they all wear it as a badge of honor, having worked there,” said Mr. Turner, who left Arthur Andersen in 1993 to work for an audit client and has run an alumni website since 1998. “Everybody says they wish the firm were still in existence.”

Some alumni keep in touch through mailing lists and social media. About 25 former Chicago-based partners, mostly from the former audit business, for years gathered for monthly lunches until the pandemic hit, said Jim Peterson, an attorney and former senior in-house counsel at Arthur Andersen. Members of the group now talk over Zoom once a month, Mr. Peterson said.

The Arthur Andersen name also lives on through an assortment of scattered objects, including a used stapler that’s up for sale on eBay for $2,500. The University of Illinois Urbana-Champaign displays Arthur Andersen memorabilia, including a set of wooden double doors from outside Mr. Andersen’s Chicago office that inspired one of the company’s logos. Other items, mostly documents and photos, are stored at Northwestern University.

Kristen Andersen, a great-granddaughter of Mr. Andersen, has an oil painting of him in her Illinois home that for years adorned a wall at the firm’s global training facility in St. Charles, Ill. Ms. Andersen said she was offered the doors, but declined. “I mean, where would I put big wooden doors?” she said.

Ms. Andersen, who worked as a senior manager at Arthur Andersen in the 1990s, said the firm’s demise was “one of the biggest professional tragedies in history.”