What happens if a dvija touches a dog? If it's sinful what is the prayaschitta? If it causes asaucha what is the method of purification?
Dogs are considered unclean as per vedas
4. 'But, surely, there are three unclean animals, a vicious boar, a vicious ram and a dog: if any one of these runs about between (the fires) whilst the Agnihotra-offering is put on (the fire), what rite and what expiation would there be in that case?'
31. And whilst not coming into contact with Sûdras and remains of food; for this Gharma is he that shines yonder, and he is excellence, truth, and light; but woman, the Sûdra, the dog, and the black bird (the crow), are untruth: he should not look at these, lest he should mingle excellence and sin, light and darkness, truth and untruth.
Expiation for dvijas due to physical contact with dogs as per padmapurANa & garuDapurANa
32. A man should bathe after having touched (i.e. if he touches) a fallen man, or a leper, or a cāṇḍāla eating the flesh of cows, or a dog, or a woman in her menses, or a bhilla.
A Brahmana having touched a dog, a shudra, or any other beast, or a woman in her menses, before washing his face after a meal, shall regain his purity by fasting for a day, and by taking Panchagavyam.
yudhishthira dog story does not invalidate any of the above as that story is about sacrifice for a dependent living being during final stage of life and not impurities associated with dogs
"Yudhishthira said, ‘It has been said that the abandonment of one that is devoted is infinitely sinful. It is equal to the sin that one incurs by slaying a Brahmana.