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The United States Postal Service does not cease operations during any Federal lapse in appropriations as it is funded through a permanent no-year appropriation.
In contrast, the U.S. Postal Service Office of Inspector General (OIG) receives an annual appropriation which is derived from the Postal Service Fund and not the U.S. Treasury.
The OIG’s annual appropriation is no-year funding. Therefore, if previously appropriated no-year funds are available, the OIG will continue operations during a lapse until such funds are depleted.
https://postaltimes.com/wp-content/uploads/2022/09/USPSOIG_Updated_Shutdown_Plan_FY2023.pdf