Hundreds of thousands of federal employees could collect late-pay penalties of at least $1,160 each — on top of anticipated back pay — after missing a second paycheck Friday due to the ongoing partial government shutdown.

The supplemental pay is being sought under a Great Depression-era law that authorizes damages for workers who are not paid on time, with potential government liability nearing $500 million as workers end a second pay cycle without a check.

A law firm representing workers suing under the Fair Labor Standards Act began a lawsuit sign-up drive Thursday on 2018governmentshutdown.com. FLSA lawsuits require opt-in, and many workers missed an opportunity to join a successful FLSA lawsuit following the 2013 federal shutdown, which resulted in four days of extra pay in addition to back pay.

Heidi Burakiewicz, the lead attorney on the current case and the successful post-2013 lawsuit, said most workers deemed "essential" are entitled to a penalty that pays them minimum wage for all of the hours they were forced to work without pay. Workers doing overtime would be paid the overtime a second time if the lawsuit is successful.

[Read more: Shutdown would cut US growth 'to zero' if it lasts too long, JPMorgan says]

The $1,160 that most "essential" workers can expect is calculated by multiplying the $7.25 federal minimum wage by 160 hours — the amount of time a full-time worker would have worked during two pay cycles.

Workers who clocked more than 40 hours a week could get much larger checks. "If you’re one of those people working a lot of overtime, the value of this lawsuit is a lot more than $1,100," Burakiewicz said.

Burakiewicz works closely with Federal Bureau of Prisons employees, almost all of whom are deemed essential, and said she was told that at one prison, 60 staff members worked overtime in a single shift.

Some employees, particularly those in management positions, are not eligible for late-pay penalties under the FLSA, Burakiewicz said. But she believes most of the 420,000 unpaid workers originally deemed essential qualify to join in the lawsuit. She notes additional workers have been called back to work after originally being furloughed, including Internal Revenue Service employees asked to return to process tax returns.

Furloughed workers are not entitled to damages under the FLSA, though they are likely to receive back pay when President Trump and congressional Democrats end a standoff over Mexico border wall funds.

A Justice Department spokeswoman declined to comment on the litigation, but there's reason for optimism for workers suing the government.

After the 2013 shutdown, Burakiewicz won a 2017 ruling from the U.S. Court of Federal Claims that workers deemed "essential" were entitled to penalties. The 25,000 employees who opted into that lawsuit have not yet been paid the penalty, however. Their payday was stalled by a four-year legal challenge — with the government unsuccessfully arguing that the Antideficiency Act, which prohibits spending without congressional appropriation, provided conflicting legal guidance — and by complex ongoing calculations of what they should get.

"From our perspective, the legal issues are identical," Burakiewicz said. Because of the 2017 ruling, which the Justice Department did not appeal, she believes the new lawsuit, filed on Dec. 31 before the opt-in drive began Thursday, could move through the courts more quickly.

Burakiewicz said that far from a greed-motivated play, the lawsuit is guided by a desire to help workers who have suffered.

About 10,000 people have contacted her law firm during the shutdown, Burakiewicz said. One worker said they were afraid to spend their final $200 on transportation to work, rather than on food for their children. Another was unable to pay for medical treatment needed due to a life-threatening condition, she said.

"It's hard for me to articulate how badly people are suffering now," Burakiewicz said. "People are having to make very tough decisions: Do I pay the electric bill? Do I pay with my credit card so I have food for my kids? People are in survival mode. That’s exactly why Congress created this in 1938. They imagined if people were not paid on time, they are going to suffer harm."