Civilian employees of the Federal government that are furloughed due to the shutdown can file for unemployment benefits from the State of Hawaii. Most states do offer unemployment benefits in these types of cases.
The Department of Labor and Industrial Relations (DLIR) recommends claimants file online at uiclaims.hawaii.gov to avoid long wait times.
You can also file by phone using the instructions at this link (PDF).
If you are not in the State of Hawaii, you can use this site, www.servicelocator.org, to find contact information for your state.
Note that you may need past pay statements to establish your unemployment claim due to Federal systems being unavailable due to the shutdown.
The U.S. Department of Labor issued a fact sheet (PDF) advising employees that they may file for unemployment benefits on the first day of their furlough. However, it may take two to three weeks for the claims to be processed.
DLNR states on their website that “If Congress decides employees who were previously placed on non pay status shall be paid for the time not worked, any benefits paid will be an overpayment and you may be required to repay any overpaid unemployment benefits during the period of your furlough.”