The term 'tailless pet' can be summarized by two crossword solutions: MANX (4 letters) and Manxcat (7 letters). The MANX is a breed of domestic cat that originated on the Isle of Man, an island located in the Irish Sea between Great Britain and Ireland. The MANX is known for its taillessness, which is caused by a genetic mutation. The Manxcat is a breed of cat that is a cross between a MANX and another breed of cat. It is also tailless due to the MANX gene.