
Yes they do exist - I own one. He was in rescue because of his inability to deal with other dogs (and cats), children and some people. Despite employing various professionals I was finally advised that some dogs - this one included - can't ever change their behaviour.
I have managed to improve him somewhat but he has some serious aggression problems. Not all of these are possibly his fault as he has an aversion to feet and newspapers so I suspect he has probably been whacked at some point which hasn't helped.
I can only manage his behaviour in a way that I continue to train, train, train and avoid other animals and tricky situations where possible. If children are around I muzzle him. It's not an answer to the problem but it's what I have to do. I have no doubt that were I to send him back to rescue he would end up there for ever or be put down. Thankfully because of my own situation I am able to keep him but he is a challenge.
CG