Sara, I am so sorry. A cat with a broken neck can live, but it would need a lot of care. My question....... Is Fluffy suffering? Can he walk? Treating a cat with a broken neck would involve veterinary care and I know that you just went through a traumatic experience. Surgery may be required. But at this point, I would assess the situation and I know this is hard, but if he was suffering and had no quality of life, I would consider putting him to sleep.