Social Security is what's called mandatory spending. The benefits are guaranteed by law, and aren't subject to yearly funding by Congress. But the administrative costs of the program are paid by the annual budget. If the government shuts down, Social Security payments would probably still go out, but there could be delays and new claims may be not be processed. In the 1995 government shutdown, Social Security eventually recalled more employees to help with the backlog of new applications as the stoppage dragged on.
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