According to this link, the government is under no obligation to offer back pay to workers who are on furlough during the shutdown 
:
After previous shutdowns, Congress has passed measures giving back pay to furloughed employees and essential employees who worked during the shutdown. That isn’t guaranteed this time, though.
Rep. Mark Meadows (R-N.C.) said federal employees knew when they took their jobs that a government shutdown was possible and that they’ll likely be paid.
“It’s actually part of what you do when you sign up for any public service position and it’s not lost on me, in terms of the potential hardship, but at the same time, they know that they would be required to work,” he said Thursday.
Democrats note that many workers live from paycheck to paycheck, so even if Congress provides back pay, some will suffer significant hardship. They have already begun lambasting Republicans over how the shutdown will affect workers.
In a tweet, Sen. Tim Kaine (D-Va.) said, ".@realDonaldTrump has no concept of the hard work our federal employees do every day to keep the country running. Forcing 800,000 of them to spend the holidays unsure about their next paycheck is cruel.”
www.latimes.com/politics/la-na-pol-congress-shutdown-20181221-story.html