The phrase "were on case" means that someone is actively investigating a situation or problem. Antonyms for this phrase could include "ignorant," "unaware," or "disinterested." These words describe a lack of attention or involvement in a particular matter. Other antonyms could be "inactive," "lazy," or "idle," which suggest a lack of effort or motivation to address a problem. In contrast, synonyms for "were on case" might be "investigating," "probing," or "examining," which indicate a focused effort to find a solution. These words suggest a sense of urgency and action, which is the opposite of the antonyms described.