UNEMPLOYMENT INSURANCE - WHAT HAPPENS IF EMPLOYER DOES NOT PAY TAXES

This is an issue I am dealing with for a charity. Let us start from the beginning. From the DOL website (emphasis supplied):

"Unemployment insurance is temporary income for eligible workers who become unemployed through no fault of their own and who are ready, willing, and able to work. You must have sufficient work and wages in covered employment. In New York State, the money for unemployment insurance benefits comes from taxes paid by employers. No deductions are ever made from a worker's paycheck for unemployment insurance. It is the Department of Labor that determines whether an unemployed worker qualifies for unemployment. "