Although the image of "hanging" suggests something terrible, "to leave someone hanging" is not at all a scary expression. You can use it freely. It simply means to leave someone in an unpleasant position they did not want or expect.
It can be used in countless situations. Suppose you are talking with a friend who asks to be excused for a moment because she has to go to the bathroom. She says she will be right back but never returns. She has left you hanging.
I had a friend once who, when talking on the phone, would interrupt the conversation because she had to talk to someone on another line. She would just leave you hanging there. Eventually she would return, but I considered it rude, and told her so. It was a habit for her, leaving people hanging. She kept doing it.