Partial thoughts, are thoughts that sound like they should have more to them. However they are intentionally left short to create a sense that more is to come. This creates a state of anxiety in people and their desire for closure. The sentence is more effective if you say the last part of the sentence with an increasing pitch. This indicates there is more to the story. When in fact there is no more to the story.

Here is an example:
"I saw this guy walking down the street..."

People will automatically assume there is more to this story. So they will say something like, "And then what?" The response is: "That is it. That is what I saw." This is the peak time of frustration. They may even argue with you or storm away. Be prepared to be called names.

There is actually some history behind this.

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Hehe, no, I am not going to leave you high and dry. In high school a dude I knew would always make fun of my friend. So I started doing these partial stories to the dude. He would get mad and storm off each time. I would do this several times per day. So it can be a tactic to deal with difficult people.