If you are at a loose end, you are bored because you do not have anything to do and cannot think of anything that you want to do. In American English, you usually say that you are at loose ends. Adolescents are most likely to get into trouble when they're at a loose end. A minor unresolved problem or difficulty, especially a final detail preceding the completion of something. Often used in the plural
A loose end is part of a story, situation, or crime that has not yet been explained. There are some annoying loose ends in the plot