An employee was fired for repeatedly violating our policies. Will this person be eligible for unemployment?

Unemployment compensation programs are run by individual states, so the answer will vary. Many states dictate that employees who are fired for “gross misconduct” (this is usually a serious and willful violation of company policy, including things like sexual harassment or violating the law, for example) are not eligible for unemployment benefits. However, the definition of “gross misconduct” will vary by state. You should allow your state agency to make the determination, and you should be given an opportunity to challenge their decision.