Sources close to the company said Wang took a hands-on approach to running the company although Chen tended to be its public face.
Wang Jian, 57, was injured in a fall during a business trip, and died on Tuesday, according to a brief statement.
After spending more than $40 billion on a buying spree, it become the largest shareholder in companies such as Deutsche Bank AG and Hilton.
But it racked up huge debts in the process and has since reversed course, selling assets to ease financial pressures as authorities in China cracked down on aggressive overseas deal-making by Chinese companies. Subscribe to the Standard Group SMS service by texting "NEWS" to 22840.More news: President Appoints Four (4) New Supreme Court Judges
Authorities in France have confirmed Mr Wang's death is not being treated as suspicious.
A local police chief, Hubert Meriaux, was quoted as saying by Reuters news agency that Mr Wang had been trying to get his family to take a picture of him when he fell.
"HNA Group extends deepest condolences to Mr. Wang's family and many friends".
HNA, the owner of Hainan Airlines, once symbolised the appetite of Chinese companies for assets outside of China.
Shares of jewelry maker Hifood Group Holdings, an indirect unit of HNA Group, fell 11 percent on Thursday to all-time lows, leading the slide in Hong Kong-listed stocks related to HNA whose co-chairman died in an accident two days ago.More news: Blac Chyna Dating Rumors: What We Know About Devin Haney
Mr Wang held 15 per cent of the group's shares.
Wang obtained an undergraduate degree in Aviation Management from Civil Aviation University of China in 1983, and a master's degree in business administration from Holland Maastricht School of Management in 1995, according to HNA.
Following its now-infamous acquisition spree, the group's financial struggles began to emerge in the middle of previous year, when the Chinese government began scrutinizing high-profile acquirers such as HNA, Dalian Wanda Group Co. and Anbang Insurance Group Co.
The company also published its website in monochrome as an apparent mark of respect. Also in attendance were executives at Glencore Plc, which hours later announced the US$775 million sale of a majority stake in its oil storage and logistics business to HNA.More news: Chambers signs long-term Arsenal deal