If it were a Manx Cat, they'd have had no option!!
Manx cats have a weird genetic mutation that causes them to be born with no, or short tails!
It's actually more of a genetic abnormality / nearly a deformity on an island population of cats rather than an actual characteristic. It's referred to as "Manx Syndrome" by many vets..
They also have an odd spine and oversized hind legs... http://en.wikipedia.org/wiki/Manx_(cat)