After Huang on Sunday acknowledged being unfaithful to his wife, Nvidia’s board announced an investigation into reports that he had been targeted by a foreign intelligence effort. The admission followed reporting about his relationship with a woman whom U.S. authorities concluded was a Chinese intelligence asset, according to The New York Times. The board said it had “no reason to believe that either national security or NVIDIA secrets were compromised,” but that its inquiry would examine “all available information.”

The trick for investigators, according to business and law experts, is that they are investigating, and will potentially consider ousting, perhaps the most critical executive to America’s AI success. And they will do so under a company power structure in which Huang reigns as an outsized decision-maker.

Huang is “synonymous with Nvidia, and Nvidia is synonymous with him, and he and Nvidia are synonymous with AI, so he’s bound up in the company’s identity much more than other cases,” Brian Burke, founder of Burke Law & Strategy and a corporate board advisor, told Fortune. Nvidia is “a paradigm out there that people look up to and they say, ‘Oh, I want to be like Nvidia.’ Other CEOs say, ‘I want to be like Jensen Huang.’ So, it’s really almost like a cult.”

Huang, 63, has set up a unique structure around him at Nvidia that has concentrated decision-making in his hands. He has been CEO for 33 years, astonishingly long for any company. Nvidia has no chief operating officer, and Huang has 60 direct reports, creating uncertainty about who is next in line to lead.

Huang is known to play a central role in strategic and technical decisions, and the success he’s had since the AI boom got underway in late 2022 has only strengthened his grip on the company and the AI industry at large. He has become something of a celebrity in the tech world, with followers wearing leather jackets to copy him and fans pursuing him at corporate events for a selfie or a signature. He has also gotten close to the Trump administration, which has counted on him for counsel on AI and taken him on foreign trips.

Huang is Nvidia’s largest individual shareholder, with a 3.56% stake. He leads what is the world’s second most valuable company. (Its shares sank more than 4% on Monday after he admitted to the affaire.) Nvidia has been estimated to control about 90% of the market for high-powered GPU computer chips used in AI data centers.

The company has also operated without a chief compliance officer. In a September 2022 staff at the Securities and Exchange Commission asked for more detail about board risk oversight, whether the company had such an officer and to whom that person reported, and about its overall structure. Nvidia has said it has a compliance committee made up of its chief financial officer, executive vice president of operations, and senior vice president of human resources, which it says “ensures communication of and adherence to all NVIDIA policies.”

There are few other cases, if any, that resemble Nvidia’s current situation. Corporate executives whose romantic liaisons have derailed their careers are common enough. In 2019, McDonald’s fired CEO Steve Easterbrook over a consensual relationship with an employee that violated company policy. The bigger scandal came afterward: the company discovered additional undisclosed relationships, sued to recover his exit compensation, and ultimately recovered cash and equity valued at $105 million. In this case however, the romantic liaison involves an alleged spy and the CEO of the dominant company building some of the U.S.’s most valuable technology.

Jason Schloetzer, an associate professor at Georgetown University who has studied CEO succession practices, told Fortune that Nvidia’s concentration of so much power and decision-making in Huang now makes it very vulnerable to what comes next.

“The board has made a mistake by not having a clearly outlined succession plan that’s been telegraphed to the market for a year or two,” Schloetzer said. “They find themselves at the day of reckoning, and it’s a sudden and perhaps forced one, rather than a relay situation where they have time to figure it out as they go.”

Hui Chen, a former federal prosecutor who served as the U.S. Justice Department’s first compliance counsel expert from 2015 to 2017, told Fortune that corporate risk efforts tend to focus on leaks from rank and file staff members, and companies don’t pay as much attention to similar risks by high-level executives. 

Schloetzer and other experts said it’s plausible for the board to appoint an interim CEO or have Nvidia’s lead independent director—Stephen Neal, chairman emeritus and senior counsel at law firm Cooley LLP—as interim CEO if Huang steps down. Another option for an interim could be Nvidia Chief Financial Officer Colette Kress. The concern with any next-CEO plan is how the market will receive the decision, since Huang is seen as critical to Nvidia’s success.

Huang also has children who work at Nvidia and could be options to succeed him. Spencer Huang is a director of product management, and his daughter, Madison, is a senior director of product marketing. Both have reportedly worked on robotics at the company. His son-in-law, Nico Caprez, is vice president of global AI infrastructure growth.

The board could oust Huang at the end of its investigation, or Huang could have to step down before then, Burke said. He could also leave the CEO role but stay on in another capacity.

In media interviews over the years, Huang has dismissed conventional succession planning, saying his approach is to continually transfer his knowledge to colleagues. He has also said he hopes Nvidia’s next CEO already works at the company, even though Nvidia has not publicly identified a successor.