SOLUTION:
When possible, lift hoop with as little tug on the fabric as possible.  Using a pointed craft blade that is mounted to a pen-like handle, place the blade close to the needle plate and cut threads a little at a time, using extreme care to not cut the fabric.  (If you're hand is unsteady, it may be best to use a blade that is slightly dull.)  If fabric has fallen into the hole, it's best to try cutting the threads from below the needle plate.  Sometimes it's even possible to remove stitching from the top of the garment by cutting only the last few stitches and free the hooped fabric.  After releasing the hoop, be sure to clean all stray threads from the bobbin area.