Drugs = welfare = drugs.
They can't hold down a job because they live for their next fix and they are willing to lie, cheat and steal, pawn all of their possessions, destroy all relationships and people who care about them, and live on the street, all to get their drugs.
The basic needs and instincts for basic survival (consuming food, procreation, maintaining health, love, relationships, family) are replaced by a chemical that short-circuits the brain. Pretty insidious.
As I said, "even if there is a correlation, how do we know it's not the welfare that causes the drug use - or that both being on welfare and using drugs are caused by a third factor such as a poor attitude toward life?"