What ways can the government ensure that the it offers is received only by the people who are in need

Put a system in place that sets the poverty level and anyone under that level can receive aide.  Also make sure that the person is providing proof of needs.  They should have to prove their income, their bills, their debt, and their need. They need to verify information has not changed after a specific time frame.  So they need to be sure that they are monitoring the people who have aide and how they are using it.  Like if you were making less than 10,000 a year and now you make 24,000; you would not qualify anymore. 

Iam not sure sorry