The word that comes to mind is 'diplomacy' but I don't believe that is quite it. It is a practice that's seems more nuanced in Asian cultures than Western. For instance, if a person is fired, rather of publicly stating the individual was fired, the person is allowed to say they wish to pursue other interests or something less harsh. It's a bit of an unwritten and unstated custom that allows the a person in a more superior social role to allow the other individual to basically save face.
This is called a courtesy: a general allowance despite the facts
In your example the person is being given a courtesy by being allowed to resign rather than being fired.
In a general sense, what we use in such a situation would be a euphemism. To say something less straight-forward and harsh (harsh on oneself or on others), we use a euphemism.
Wikipedia cites "influential Chinese authors" on the subject of face. One, Lin Yutang, is quoted on the practice of granting: "grant face; give (someone) a chance to regain lost honor." A guide for non-natives doing business in China reads: "Directly rejecting a request may cause considerable face-loss since it signals that the person receiving the request is not granting face to the person making the request. Chinese face-saving practices allow all members of a social interaction to preserve dignity and to avoid embarrassment."