SEOUL—A South Korean court granted a reprieve to the head of the country’s flagship airline early Friday, denying prosecutors an arrest warrant based on multiple allegations, including embezzlement and fraud.
It was a rare bit of good news for Cho Yang-ho, the head of Korean Air Lines Co. 003490 0.72% He is the patriarch of a clan whose string of public misdeeds have helped fuel a wave of anger aimed at the family-controlled conglomerates that dominate South Korea’s economy.
Korean Air has been in the hot seat as prosecutors and the public focus on a number of allegations involving the Cho family, including illegal hiring, luxury-goods smuggling, violent outbursts at subordinates and other corporate malfeasance.
Mr. Cho isn’t out of the woods yet, as he will have to defend himself against pending allegations. But his reprieve comes at a difficult moment for Korean Air and Asiana Airlines Inc., 020560 0.61% South Korea’s other major carrier.
In recent months, shares of both airlines have tumbled due to higher fuel prices, a weaker Korean won and other headwinds.
Since recently hitting a high for the quarter on June 12, Korean Air shares have fallen 17% over the past three weeks. Asiana shares have dropped by nearly 20% over that same period of time. Meanwhile, Jin Air Co. , a discount carrier affiliated with Korean Air, has dropped 24%.
Korean Air has a market capitalization of about $2.3 billion, down by more than 25% from the end of January. The company’s shares were slightly higher Friday morning.
All three airlines have had recent safety mishaps, including a collision between a Korean Air plane and Asiana jet on a runway in Seoul last week.
In addition, Asiana hasn’t been able to serve meals on some of its planes since Sunday after switching catering suppliers.
Park Sam-koo, chairman of Asiana parent Kumho Asiana Group—one of the country’s most prominent conglomerates—has apologized. But employees have organized a protest in Seoul’s main square on Friday where they say they will expose more corporate wrongdoing.
In May, more than a hundred masked Korean Air employees called for the Cho family to step down.
When Mr. Cho said he would resign as CEO of Jin Air shortly after the protest, shares of Jin Air and Korean Air rose 7.3% and 3.5%, respectively. A spokesman at Jin Air said Mr. Cho’s resignation was aimed at “strengthening responsible management.”
Mr. Cho, 69, is still chairman of Korean Air and its parent, Hanjin Group. He is accused of embezzlement, breach of trust, fraud and violating tax laws.
The investigation into Mr. Cho follows incidents involving his two daughters—who have held senior positions at Hanjin Group—and his wife.
The trouble for the Cho family began in 2014 when daughter Hyun-ah, also known as Heather, ordered a Korean Air jet to turn around at John F. Kennedy International Airport in New York after berating a flight attendant for serving her macadamia nuts in a bag, rather than on a plate.
She was imprisoned for violating South Korean aviation laws but released on a suspended sentence after 10 months. In recent months, however, she has been questioned by authorities for allegedly smuggling luxury goods from overseas without paying taxes.
Mr. Cho’s second daughter Hyun-min, also known as Emily, was questioned by authorities in April after allegedly throwing water at an employee of an advertising agency during a meeting.
Emily Cho, 34, a former vice president at Korean Air and board member at Jin Air, was questioned by police on allegations of assault.
Mr. Cho’s wife, Lee Myung-hee, was summoned for questioning by police for allegedly abusing and berating workers, including Hanjin employees. She was also questioned for illegally hiring foreign domestic workers.
Though Mr. Cho’s wife and daughters haven’t been charged, the allegations have been followed closely by South Korean media, sparking anger against the behavior of second- and third-generation heirs at the nation’s largest business empires.
A spokesman at Korean Air declined to comment. No lawyers representing Mr. Cho or other family members could be reached for comment.
Altogether, Hanjin Group’s four listed affiliates have lost about $1.4 billion in market capitalization since Emily Cho’s “water rage” incident in April.
Jin Air, in particular, has suffered. Last month, it was fined $5.3 million for failing to properly address problems with a jet engine and plane door.
Now, South Korean regulators are weighing whether to strip Jin Air of an operating license for making Emily, a U.S. citizen, a board member between 2010 and 2016. South Korean aviation law prohibits foreigners from serving as board members at national airlines.
South Korean regulators haven't said when they will decide Jin Air’s fate. A Jin Air spokeswoman said the company will cooperate with authorities at upcoming hearings.
Write to Eun-Young Jeong at Eun-Young.Jeong@wsj.com