Hoffman? Detective Sing?

Are you referring to Billy the Puppet?

If you don't know, he's not an actual person.

We have „The Pig“, a very good pick for a Saw killer, as the character was actually into directly killing. Jigsaw himself gave his victims at least some kind of a twisted Chance and he would be too fragile. That puppet (white face with the red markings on cheeks) is only a puppet and is part of the Pigs power in DbD, as he sits on the jigsaw boxes and even makes the iconic laugh.