The structure literally translates to “not finish-finish it.” By not resolving the matter, it is paradoxically “settled” by being left unsettled. The lack of a conclusion becomes the conclusion itself.
The connotation of `不了了之` is typically neutral to slightly negative. It points to a lack of resolution, which can imply inefficiency, avoidance, or injustice. However, in certain social contexts, it's understood as a necessary or even skillful way of handling a delicate situation.