anapodoton
According to Wikipedia:
An anapodoton [is] a thought [that’s] interrupted or discontinued before it is fully expressed. It is a figure of speech or discourse that is an incomplete sentence[…] As an intentional rhetorical device, it is generally used for set phrases, where the full form is understood, and would thus be tedious to spell out, as in “When in Rome [[do as the Romans do]].”
(Where double square brackets indicate square brackets in the original.)
I like using this rhetorical device in fiction—having a character say part of a widely known phrase and leaving the rest of it for the other characters, and the reader, to fill in. But of course that can backfire if the reader isn’t familiar with the phrase.