Aposiopesis
a-pos-i-o-pee’-sis / From Greek: aposiopao “to be silent after speaking, observe a deliberate silence”
Also known as: praecisio, reticentia, obticentia, interruptio, figure of silence
Breaking off suddenly in the middle of speaking, usually to portray being overcome with emotion.
Examples:
In Shakespeare's Julius Caesar, Antony interrupts his own speech at Caesar's funeral:
"O judgment! thou art fled to brutish beasts,
And men have lost their reason. Bear with me,
My heart is in the coffin there with Caesar,
And I must pause till it come back to me."
—Shakespeare, Julius Caesar 3.2.104-107