Etymology

close the loop

Today it means: To follow up; to tie up loose ends; to resolve. Full definition →

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The story

Evidently by loose extension from control theory proper, regarding closed-loop control ("close the loop": "announce that enough feedback has been collected to successfully plan the system's next action"). Possibly influenced by the computer programming sense of "loop," in which program control will flow forever around an infinite loop until something is done to break (or exit) that loop.

Etymology from Wiktionary, CC BY-SA 4.0.