A person familiar with Nunez's immigration status told the Herald that Nunez's return to the Dominican Republic was prompted by the revelation that he was using an assumed name.
Nunez might have been aware of the problem as far back as July, the source told The Herald.
"I can't yet comment," said Nunez's agent, Andy Mota, told the Herald. "This is very recent. I don't want to say anything at all."
The Associated Press reported that Nunez's real name is Juan Carlos Oviedo, and he is 29, a year older than the age listed in the Marlins' media guide.
For Nunez to be reinstated from the restricted list, he must rectify the immigration issue that apparently has to do with missing paperwork.
Nunez, who has 36 saves, is entering his final season of arbitration eligibility and stands to earn about $6 million next season. The Marlins will decide after the season if they will bring Nunez back for 2011.