The word "be-dogged" implies being relentlessly pursued or harassed by someone or something. Its antonyms would be words that describe a lack of pursuit or harassment. Examples of antonyms for this word include unbothered, untroubled, unchased, and unharassed. These words express a state of being free from any kind of persistent pursuit or harassment. Other antonyms could include peaceful, relaxed, unthreatened, and serene. These opposing words serve to provide a balance to the idea of being pursued, by suggesting that there are alternative states of being where one can feel safe and free from danger.