Like all good sci-fi the idea is vaguely proposed but never explained. Perhaps he was sent there to "observe" Vic, as Lou tells him they have been doing for some time, and he rebelled against their control. That, along with the "Committee's" seeming obsession with recounting facts and figures almanac-style, makes me believe that the dog actually came from the shelter. How exactly the dog knows so much or is able to speak to Vic is never really explained, but I think there's a clue in that Lou (Jason Robards, Jr.) believes that Vic has spoken to a dog he encounters in the shelter. Just to run through some of the aspects of the film that I enjoyed, I really liked Tim McIntire's voice work as the dog, perfectly crisp like a cranky old man.
But when Vic (or as the dog calls him, Albert) is lured into a surreal society living in a large bomb shelter, their friendship is threatened and Vic is almost forced to become a sort of sexual machine for the good of the State. They live in a post-apocalyptic wasteland where Phoenix Arizona used to be, and hunt women and food with the same predatory zeal.
From Ellison we get a very dark tale about a strangely human dog and his boy. Its source material is a novella by Harlan Ellison, a writer who's recognized by many in the sci-fi community as a master on the same playing field of "psychological sci-fi" as Ray Bradbury and Philip K.
Surely those who were looking for nothing more than what Hollywood usually delivers when they invoke the words "science fiction" were disappointed, because this movie resembles the usual horror or action film masquerading as sci-fi very little.