Unfortunately, you will probably have to pay. Liability, or the financial obligation to pay, depends on fault, such as negligence. Negligence means unreasonable carelessness, or not taking reasonable precautions. Having the invisible/electric fence for a dog is a *reasonable* precaution--"reasonable" just means what it sounds like; it does not mean "foolproof" or "perfect." If the owners had the dog on an invisible/electric fence, they were taking reasonable precautions; the fact that those precautions failed this time will most likely not make them liable, since the law does not hold people to the standard of perfect of infallible care.