Such a person is often called a cat's-paw, based on the fable of the monkey who used a cat's paw to pull chestnuts out of the fire. In politics, a word sometimes used is stalking-horse, since - when stalking deer- the animals are not 'spooked' by a horse and, by hiding behind it, the hunters can get closer to their prey. Mind you, in the latter case, the supposed rival candidate is usually aware that he is being so used.
Is that the sort of thing you're after?