This is blatantly false. The majority of states will only provide benefits if the employee quit under certain circumstances. These circumstances are generally if the employee quits on direct orders from a health care professional or if the employee has reported sexual harassment to the employer and the employer refuses to take steps to make the workplace free of such harassment.
Your state may have additional requirements. If the employee has been terminated, the employer may fight against the employee getting unemployment benefits. The rules for getting these benefits are further discussed in Chapter 12. State law governs the requirements for getting unemployment benefits.