Federal employees with work permits are eligible for state unemployment and can file a claim the first week they are out of work. Many government contractors are also eligible.
"Actually, I submitted my unemployment application on Monday," Stann Kaplan, an application analyst with the Department of Housing and Urban Development, told CNN. "When I filed, they asked me why I did not do it before, I just said I was waiting to see if they pay us or if this closing will be over."
Not all suspended federal workers can claim unemployment. Employees who are considered essential and who currently work without pay are not eligible.
June Bencebi, a case manager at the Federal Detention Center in New York, is one of them.
"We are in the same situation as a dispossessed worker, and they do not pay us, I feel we should be able to collect unemployment because we do not receive any income inside our homes," said Bencebi, who is the Treasurer of his local union.
Bencebi says that many of his colleagues are running out of work, replicating a pattern seen in the Transportation Security Administration.
"I'm already having [union] the members tell me that they have been feeding their children with peanut butter and jelly sandwiches, "said Bencebi. Once they arrive on Saturdays and Sundays, I think more people will not be able to go to work because they will not have money, "Most of our staff live from check to check."
The American Federation of Government Employees, the largest federal union of employees, says that many of its members have already applied for unemployment and expect the number to continue to rise if the closure does not end.
Larry Hirsch is the Vice President of AFGE Local 913 in New York and is a senior HUD planning and development representative. So far, it has been able to stay afloat without unemployment checks, but that could change if the closure is prolonged.
"If we're still here in the spring, I'll start thinking about it," Hirsch said. "I want to work, I want to do my work, five days a week, we are in public service, you want to serve the public."
Kate Trafecante from CNN contributed to this report.