Unfortunately “drug tests” are not useful markers of recent drug use for some recreational drugs. It would be nice if they were, but other, less straightforward measures may be needed in some cases. Proof may be difficult in some cases but the principles of requiring responsibility for drug use and denying drug use to those who can be reasonably proven to be irresponsible, should be the goals.
In heavy users marijuana can be detected in urine for a month, less time for light users. It can be detected longer in people than any other illegal drug. So yes it could be used to screen welfare applicants and those receiving such benefits.