Is it right for the Company to terminate an employee’s service while the employee is on annual leave?
Termination process shall be carried out officially and sensitively. Personally, I do not support on terminate employee service while they are on annual leave, it is not feasible to just call the employee and tell him/her that "your service has been terminated".
As a good practice, the employee shall be informed about their mistake / performance issue, by going through the steps of disciplinary procedures.
Although it is stated in the employment contract that both parties can terminate the service by giving the notice or salary in lieu, but if HR does not carry out the good practice, this will definately affect the company reputation and also the morale of the rest of employees. All employees are aware that their service can be terminated anytime by company by giving salary-in lieu of notice.