I don't know if there's an exact phrase for it, but if a character whose death is central to the plot is an on-screen presence and not simply explained as backstory, it is generally to establish empathy for the victim and to make the killer seem all the more sadistic for killing such a person. Usually that death is used to motivate the hero to fight when before they might have been reluctant, thus moving the hero's arc along quickly and efficiently.

When it involves a doomed female character, it is often referred to as "fridging," but this connotes an element of sexism in the device, where women are killed off for the motivation of their male counterpart.

I don't know if anything I said there sounded like what you were looking for. I truly do not know of a phrase for this device that doesn't have the negative connotation.