A Maltese dog
The Maltese dog is not a creature that could exist naturally. Just about every trait that was bred into these dogs would be a detriment to their survival without human assistance. Their size would make them a choice meal for larger predators. They have been bred for docility and friendliness, likely at the loss for behavioral traits beneficial to solo or pack hunting. A Maltese that escapes or otherwise becomes separated from its owner's care will not last long in the harsh reality of the natural world. Assuming it makes it past the automotive gauntlet into a natural area, it would only be a matter of time before it is picked off by a bird of prey or other carnivore. Even it it manages to elude predation, its stubby legs and cuddly nature preclude its ability to capture food. These dogs are an abomination of nature, yet humans see enough value in their traits to continue investing resources into sustaining their existence.
The Maltese was bred for a docile and gentle temperament that would prohibit its existence in the natural world without human intervention. The Cordoba Fighting Dog, on the other hand, is a bred for traits on the opposite extreme of the aggression spectrum. An amalgamation of the Mastiff, Bull Terrier, Boxer, and Old English Bulldog, the Cordoba was bred to dominate the dog fighting pit. The dogs were selected to display extreme intraspecific aggression, so extreme that the males and females of the breed would rather fight than mate. It is reported that the dogs were capable of hunting in male and female duos, but larger packs would suffer from infighting. A combination of deaths in the pit and reluctance to mate led to the breed's extinct status (although Wikipedia confusingly notes that a number of the breed continues to exist in small numbers in Argentina). The Cordoba, like the Maltese, was bred for such extreme behavior that its ability to survive was brought into question.
A video about the Belyaev Silver Fox domestication experiment, which has led to insights into the nature of the relationship between man and the domestic dog.
For many domestic breeds, man has imposed a genetic leash that prevents the animals from surviving without man's assistance. It should be noted that many breeds are capable of going feral and thriving, for example the Australian dingo. However, these breeds are often the ones that more closely resemble the phenotype of their wild ancestors than that of toy dog breeds. Man's plant and animal domesticates are reliant on our intervention for their survival, and so are we reliant on them to a large extent. Our complex and densely populated societies are sustained by a relatively small number (on the scale of global biodiversity) of domesticates. Some of these domesticates, such as maize, wheat, and rice, occupy disproportionally important roles in agriculture. Domestication has clearly played an important role in determining the developmental trajectory of domesticated plants and animals as well as man. We know now of many effects that pets can have on the lives of pet owners, for example, pet owners enjoy a number of health benefits. How much do you think the behavior that we have bred into our domesticated animals affects our own?