A contract employee may be eligible for ESI benefits for accidental cases within a year, depending on the specific terms of their contract and the regulations governing such benefits. It's essential for the employer and the employee to review the contract thoroughly and consult with the HR department or relevant authorities to determine the coverage and eligibility criteria for accidental cases under the ESI scheme. Additionally, seeking clarification from the insurance provider or legal counsel can help in understanding the extent of coverage available to contract employees in such situations.