Amtrak, like USPS, is an independent government established "corporation" which is only partially funded (subsidized) by government grants (operating subsidies, and capital grants) through Federal appropriations.

Amtrak (aka the National Rail Passenger Corporation) is not a Federal agency, like say the National Parks Service, and thus is not directly affected by the failure of Congress to adopt a budget appropriation resolution, or a budget continuing resolution, and unlike the National Park Service will not shut down, if Congress fails to do its job.

Amtrak actually earns significant revenues, vastly greater than the "gubmint" subsidy it receives from the Federal "gubmint", and last year was a record year for ridership, revenues, and "farebox recovery". This revenue comes from things like selling tickets to all of those folks going the Santa Barbara today, on full trains. So Amtrak has cash flow and reserves to keep operating for a while without Congress adopting a budget resolution.

Amtrak 2017 Earnings

Will Amtrak be "safe" if the government shuts down..... It will keep operating, yes. And, is you mean "safe", also yes, If people pay attention and follow the rules, US intercity passenger rail is one of the safest modes of transport per passenger mile.....

I don't know if that helps. And, I don't know from your handle, if it was even supposed to.... but, if it was a real question, you have an answer.