FBI Director Voyles: Are you asking me to ignore a suspect, Mr President?
The President: If the press...gets wind of what you're after and starts digging, I'll be--we'll be crucified.
FBI Director Voyles: So you're asking me to back off?
The President: Back off and chase the real suspects. Ignore it for a few weeks, that's all.
--The Pelican Brief
In the context of allegations that Donald Trump obstructed justice by interfering in various DOJ and NSA investigations, Judge Nap discusses the concept of the unitary executive.
Unitary executive theory holds that the president is the chief executive officer of the federal government and, therefore, everyone in the executive branch works for him. Because the president is the only one in the executive branch that is accountable to voters, there can be no people in the branch who are not under the chief executive's authority. It this weren't so, then vast areas of governance would not be accountable to the people. This would violate the right of people to be governed by the consent of the governed.
Under unitary executive theory, the director of the FBI and other directors of various agencies in the executive branch serve at the pleasure of the president. They are obliged to follow all orders and requests of the president or resign. Upon resignation, they may reveal the reasons for the resignations.
In opposition to unitary executive theory is the argument that people who serve underneath the president have an ethical duty to pursue wrongdoing even if the president demands or requests that they 'back off.' This is especially the case if the president is suspected of being involved in the wrongdoing. This argument posits that the president does not need to intervene because he ultimately has the power of the pardon, and can constitutionally terminate sentences of those who may be convicted of crimes prosecuted by executive branch agencies.
Here is an informative give-and-take between the Judge and Juan Williams on the matter in the context of Trump's troubles.