Hmm, some purebred dogs yes. They can have quite awful lives because of genetic diseases. But domestication, besides the fact it was done by our pre-human ancestors, is not the same. Modern thinking sees the domestication of dogs more as a co-evolution of humans and dogs.
Dogs can function quite well in their natural environment (in close proximity to humans); white Bengal tigers will die very, very quickly in the wild. The mutation is non-adaptive.
You mean like cats? (That's not a rhetorical question, by the way. When you domesticate tigers, would they be very different from what we now consider a cat?)
That's sort of the process we had to get the bengal (hybrid asian leopard cat and housecat), which is considered a domestic cat after 4 generations.
Same thing has been done with servals ("savannah cat"); I can only imagine how awesome/terrifying it would be with other lesser wild cats, although I think there are enough differences between the great cats and domestic cats to make it difficult/impossible to do naturally (tiger/cat or leopard/cat cross).