Police have not said how many victims are involved, but officials are warning the public to remain vigilant as the investigation continues.
The partial government shutdown that started Saturday is vastly different from the record closure in the fall.
New work requirements for SNAP are set to go into effect on Feb. 1, and it could mean that millions of Americans lose their benefits.
It's part of a push by Health Secretary Robert F. Kennedy Jr. and Agriculture Secretary Brooke Rollins to urge states to strip foods regarded as unhealthy from the $100 billion federal program.
According to authorities, 36-year-old Andre Streater stole the personal information of more than 40 individuals this past summer and submitted fraudulent SNAP applications.
The Trump administration said it will move to withhold SNAP food aid from recipients in most Democratic-controlled states starting next week unless they provide information on those receiving the assistance.