The rights of the employee after the expiration of a fixed-term employment contract include entitlement to compensation for unfair termination, which equals the salary for the remaining period of the contract with a minimum of two months' salary, and an end-of-service gratuity calculated based on the length of service and the last salary. Additionally, the worker is entitled to receive their full salary and other entitlements within a week after the contract ends, while female employees are entitled to full gratuity in cases of marriage or childbirth during the specified periods.