Collected Unemployment After Started New Job

My question involves unemployment benefits for the state of: new york
my cousin collect 5 or 6 weeks unemployment after starting a new job; he said he was so scared of getting fired the first few weeks he just kept collecting, then stopped. after getting some kind of letter from unemployment, he paid back all he owed but he is convinced he may be prosecuted; i told him if he paid it back in timely manner, why should they prosecute

The UI office is much more interested in getting their money back than in prosecuting. It is highly unlikely that he will be prosecuted if he has paid back everything. They reserve prosecution for those who refuse to cooperate.