Here's why they might want your pet:
To "live train" fighting dogs. The animal you expected to be treated humanely is used to bait a fighting dog and is literally torn to pieces.
To sell to a Class-B Dealer who then resells the animal to a research facility. People who practice the despicable act of rounding up strays to sell them are referred to as "Bunchers" who typically keep the animals they find in the most miserable conditions you can imagine. Most of the time these animals are neglected, kept in cramped, unsanitary conditions and often become sick and diseased. A quick Internet search will give you a lot of information on the subject of bunchers. The animals who survive their horrific stay at a buncher's kennel end up at animal research labs where they continue to suffer more pain and discomfort until the researchers euthanize them after they've served their purpose.
Often the pet is used as live food or bait for exotics like snakes or alligators.
Used for breeding stock in a "Puppy Mill". The living conditions in most of these establishments are deplorable. Bitches have continuous litters, one after the another.
Sacrificed in cult rituals. Some people find this hard to believe, but the FBI has many files documenting this kind of activity in our country.
Here's how you can flush out the con artists - who by the way, may come across as the most persuasive and friendliest folks you could meet. This is because they have their scam well-honed and practiced.