Those agencies which control nuisance pets are sometimes known as "the dog catcher" and/or "the pound". The agency may be municipally-run or a municipality may contract with an agency like the BC SPCA to be the dog-catcher, or the impound/disposer, or both.
These nuisance pet control agencies, including the BC SPCA, protect the public from nuisance pets such as stray dogs, cats, rabbits, etc, by collecting them (by actively picking them up, or by accepting them from the public which has caught them) and disposing of them (by selling or killing). The disposal of nuisance wildlife (rabbits and rodents, etc, are the business of frankly-named "Pest Control" companies which don't have any need, not having any animal-loving donators, to obscure why they are killing animals.