Can you receive unemployment if your company isn't paying into the state Unemployment Insurance fund?

It depends. Many, if not all, states designate employers as qualified or not as to whether they are required to pay payroll taxes to the state. Persons on commission only basis (independent contractors, real estate and insurance sales people, government employees, etc.) may not be eligible for unemployment benefits. Check with your own state's employment security office for clarificatlon. However, if they ARE required to, then you probably will and the state would go after the employer for non-compliance.