Antonyms for "supervise communications" could include "ignore" or "neglect." If someone is not supervising communications, they may be disregarding them or failing to pay attention to them altogether. Other antonyms could be "disregard," "overlook," or "abandon," as each of these words implies a lack of attention, care, or concern. In contrast to supervising, these antonyms indicate an absence of guidance or oversight. However, it is important to note that neglecting or ignoring communications can have negative consequences, so it is always better to supervise and monitor them in order to ensure that important messages are received and responded to appropriately.