Step 1: no longer provide money alone, provide them with jobs and then assistance as needed based on salary. Those who refuse the job given, quit, or intentionally cause themselves to be terminated are denied benefits.
step 2: find employers who hire illegal immigrants and offer them a choice: hire unemployed citizens or legal immigrants and the recieve some compensation or be fined for each day compliance is refused.
notes: not a perfect plan, but a begining. Some funds may have to be spent to train or educate employees, but if our tax dollars are going to be spent to help the unemployed where would we rather it be spent...to pay for someone to have a job (and needed training) or for the same person to draw benefit without having to work for it?