Consider this sentence from an article about a killing:
“Based on repeated threats on the night of, they (Rose, Ford and Liakos) decided to go on a scouting mission that was preserved on video,” Robinson said, referring to Leiteritz’s doorbell camera capturing Rose as she checked to see if Leiteritz was home just an hour before the incident.
Typically the word "of" is followed by an object. In this example, it would have been valid to say, "Based on repeated threats on the night of the killing...", where the killing is the object. However, the speaker here omitted "the killing". A listener might have wondered, "on the night of what?", but they were expected to infer that the object was the killing that was mentioned earlier and not even in the same sentence. (Although this usage does seem strange in a courtroom, where one would think that explicitness would be better to avoid any possible confusion.)
Here is another example:
A separate statement from more than 60 Republicans and Democrats who have served as Cabinet secretaries, senior White House officials and congressional chiefs of staff for the past six presidents urged the Biden administration and Congress to enact policies to help protect the Asian American community.
The signers of served in the administrations of Presidents Ronald Reagan, George H.W. Bush, Bill Clinton, George W. Bush, Barack Obama and Donald Trump. They include Elaine Chao, labor secretary under George W. Bush and transportation secretary under Trump; Obama commerce secretary Gary Locke; and Norman Mineta, who was transportation secretary under George W. Bush and commerce secretary under Clinton.
Instead of writing "The signers of the statement served...", they just wrote "The signers of served...", with the implicit object being the statement that was mentioned in the previous paragraph.
I find it interesting that Merriam-Webster does not provide any example of this usage, and they provided 26 examples for all of their definitions of the word "of".
Is there a name for this usage of "of" with an implicit object?