As for the dog, one would say that if the sacrifice is purificatory, it is sacrificed on behalf of those who use it.
"Plutarch's Lives, Volume I (of 4)"
Plutarch
The Greeks, in their purificatory rites, sacrifice dogs, and often make use of what is called Periskylakismos.
"Plutarch's Lives, Volume I (of 4)"
Plutarch
These are purificatory ceremonies.
"The Khasis"
P. R. T. Gurdon