The NRL has fined Josh Dugan $50,000 and Adam Elliott $10,000 respectively over recent incidents.
It was announced on Thursday that Dugan has been issued a breach notice for failing to comply with the game's biosecurity protocols.
According to the NRL statement, it proposes that he will also be removed from the club's biosecurity bubble in NSW. Dugan, who was fined $25,000 by the NRL for breaching the NRL's biosecurity protocols in June by visiting a Potts Points restaurant, did not travel to Queensland with the Sharks squad when it relocated recently.
Dugan is alleged to have driven to Lithgow with a friend on the evening of August 20, in contravention of the game's Level 4 Protocols.
"In considering the proposed penalty, the NRL took into account that the alleged breach was Dugan's second serious contravention of biosecurity protocols in the past two months," the NRL said in a statement.
"The NRL alleges that Dugan has shown a continued failure to comply with the protocols and poses an unacceptable risk to his teammates in the NSW bubble."
Under the NSW Public Health Order for the current COVID-19 outbreak, residents are not permitted to move outside their LGA or five kilometres from their home except for specific reasons, including work or to receive medical treatment.
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Dugan, 31, is off contract with Cronulla at the end of the season and has been told that he is not part of the club's plans for 2022 under incoming coach Craig Fitzgibbon.
He has five working days to respond to the breach notice, as does Elliott, who is alleged to have brought the game into disrepute and failed to comply with biosecurity protocols.
It is proposed that he must complete education and training on top of his fine.
"The notice alleges Elliott brought the game into disrepute after he was removed by security from a Gold Coast restaurant on August 22. It also alleges that the conduct leading to his removal breached the game's biosecurity protocols."
Broncos NRLW forward Millie Boyle has been issued with a warning regarding her conduct at the restaurant and will be given education and training regarding the obligations of players in public. NRLW players are currently not subject to biosecurity protocols.