Related to close-ended statements are close-ended questions, which can only be answered with a "yes" or "no," or another finite answer such as a location or time. These are different from open-ended questions, which invite a more narrative answer.
A closed ended statement can occur in an ongoing conversation. Instead of inspiring another question or statement by the other person in a conversation, it is usually a "yes," "no," or finite statement.
When asked, "Did you have a good weekend?" a closed ended statement would be a yes or no, rather than a detailed description of events.