A source also confirmed that the incident took place on March 11 in Georgia where AMC is filming the final season of the long-running series.
The late national beauty, described as a swimsuit rebel, was a swimsuit category winner but had refused to parade in a swimsuit during her year-long reign.
His death was not COVID-related.
“We ask that you please keep Earl/DMX and us in your thoughts, wishes, and prayers," they wrote.
The former CNN star died at Cedars-Sinai Medical Center in Los Angeles aged 87.
Jung has appeared in a number of Korean dramas, a music video for K-pop group iKON while her big-screen debut was in Golden Rainbow in 2013. She had also been working as a model.