If a dog that had its tail surgically removed due to an accident is bred with a dog with a long tail, none of their offspring will be born without tails; the genetic information for tail development is still present in the "tailless" dog, even though it cannot physically express it due to the previous surgery, so all puppies will inherit the potential for a tail from the long-tailed parent. 

Removing a physical trait like a tail through surgery or accident does not change the genetic makeup of the animal, meaning they can still pass on the genes for that trait to their offspring. If a dog with a naturally occurring "bobtail" (genetically short tail) were bred with a long-tailed dog, there might be a chance for some puppies to inherit the bobtail gene and have shorter tails, but this scenario is different from a dog that had its tail surgically removed.