Can an employer refuse to pay for unused paid time off when an employee leaves the company

Question Details:

My employer constantly reminds us that we are all at-will employees, but wants us to all sign an employee policy book which it constantly changes and add news terms and clauses to. In a recent update the employer wants to force all employees to agree to give it 4 weeks notice or they won't be paid for PTO accrued already. We've all accrued our unused under a previous policy which had no penalty or conditions. The employer still insists we don't have a contract and as such we the employees are entitled to no notice from the employer. So what do we call this 4 week requirement with this penalty? Important Notice