The phrase "are on case" suggests that someone is actively investigating or taking care of a situation. Some antonyms for this phrase might include "ignorant", "disinterested", or "apathetic". If someone is ignorant of a situation, they are completely unaware and uninvolved. Similarly, someone who is disinterested may have knowledge of the situation, but lacks concern or motivation to take action. Lastly, someone who is apathetic may have some level of interest or knowledge, but lacks any sense of urgency or responsibility to address the issue at hand. These antonyms describe individuals who are either uninformed, uncaring, or inactive, which is the opposite of someone who is "on case".