Recently I (American English speaker / academic / raised in Appalachian and Southern dialect household) noticed myself falling into a conversational pattern with coworkers where I would end a spoken sentence with a conjunction and trailing off. Here are a few examples in the spirit of what was said.
Needing to print off more fliers:
The printer doesn't seem to be working right now, so ...
Making a decision with multiple possibilities:
Should we go with the red paper, or ... ?
Picking a group of people for a trivia team:
So it should be Alice, Bob, Charlie, and ...
I attribute the trailing off to leaving an opening for further input from others. Sometimes it's because they would get the gist of what I'm saying in context and be able to reply. Sometimes it's because I really need their input. (Who am I forgetting for the trivia team? What other colors of paper are good options?)
I'm wondering if there are grammatical or linguistic explanations for this feature. A past question about a terminal "so" dealt with whether it was grammatical, but none of the options mentioned feel particularly descriptive of this feature: whether or not it's trailing off or an ellipsis, it isn't just that; it could be a kind of discourse marker but I would expect them to begin a sentence; it is somewhat like a tag question but sometimes not a question at all.
Meanwhile, this source calls it a "conjunction-ended sentence," which describes the form (a conjunction does end the sentence) but doesn't generate any other search results. Perhaps there is a better concept capturing how it's being used. It would be even better if a term would lead me to further resources on the subject.