I have to admit my question is triggered by a scene in Veep, where a security situation results in the President being surrounded by Secret Service agents (s04e02), but after spending some time on Wikipedia, I think my question is still relevant and not immediately easy to answer.

What sort of personal protection do senior non-elected officials get, such as Chiefs of Staff or other Senior Advisors? I can understand why they may not be afforded around the clock protection, but if a situation does arise, are senior advisors protected alongside the official (whether they are POTUS, Vice President, or legislators), or is the focus entirely on the elected official?

Given my relatively limited understanding of government, it seems to me that unelected officials, at least senior ones, are as vital to the running of government business / execution of policy as the elected officials they advise.