The phrase "curled tail" refers to the way a tail of an animal is shaped when it bends or loops in a rounded manner, instead of hanging straight down. Full definition
He may drop to the ground, lower his head, or curl his tail between his legs. (southkendall.com)
A too tightly curled tail in no way impacts the quality or potential for being a wonderful family companion but it may be detrimental to a show career, so such a puppy may be placed into a companion home. (havanesefanciers.com)
Northern breeds such as Alaskan Malamutes with curled tails automatically «signal» dominance to other canines, whether they truly feel that way or not. (thesprucepets.com)