Name for a literary device -- "an offer you can't refuse"

The names of literary and rhetorical devices are often very difficult to find, and I’d like to know the name – if there is one – of one I’ve tried to find a name for and failed.

Basically, it’s “an offer you can’t refuse”. (I know the phrase is tired, but it gets the point across.) I call it “empty offering”.

Offers of this type are fairly common in everyday life. Essentially, a command is given in the form of an offer which must be accepted, or a question is asked to which there is only one acceptable answer. For example, “Is nine o’clock okay for you?”, or “How is everything?” (at a restaurant). “Do you mind …?” is mostly asked just to be polite, because the person being asked is unlikely to say no. Even “How are you?” generally has only one answer, but it’s not exactly what I have in mind here.

I use “empty offering” quite often in writing. For example, a group of people facing death are given a choice: they can remain where they are and die heroically, or leave and save themselves. The offer is worded such that the group knows they must choose the former. The purpose of the offer is to make their death seem even more heroic because they were given the chance to save themselves and refused. (Think “Go tell them, traveler, in Lacedaemon, that here, in accordance with our laws, we lie.”)

Anyway, does anyone know what this is called? I’ve never found a name for it, and there are lots of names for literary devices.

I know this isn’t quite what you are seeking (it’s not the generic term), but another phrase along these lines is “Hobson’s choice,” which effectively means no choice at all. Apparently, Hobson rented out horses, and he insisted you take the next one available or none at all.

Hobson’s choice?

extortion?