I remember a joke about taking your dog's life and then killing his dog. So there seems to be a follow-up. What is this?

Then the killer asked, do you have a girlfriend? The man said no.

Then the killer killed the man, too,

Then he said, single dog is a dog, too.

The above is the second half of the joke.

In fact, there are many versions of this joke, but I didn't find it at the moment and didn't recognize it. This is only the initial version.