The short answer is yes, a bun can definitely get hurt while wearing a harness. Harnesses can be quite dangerous if a bun pulls suddenly or gets startled while wearing one.
The safest way to give your bun access to the outdoors is to set up a portable exercise pen, and to be sure your bun is trained to return to a carrier on command (even when frightened).
There are some people who will take their bunnies outside on harnesses, but in my opinion this usually seems more for the human’s enjoyment than the rabbit’s, and it probably isn’t a good fit for many bunny personalities. If you do choose to work on harness training, it has to be done very slowly, starting indoors. First the bun has to get very used to wearing the harness indoors, and well trained to come to you and/or to a carrier on command while wearing it.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.