Dear Deiveegan,
What's your confusion in this case of unauthorised absence?
The employee has, in the first place, breached the contract of employment by absenting himself without prior approval of the employer or any intimation from his side thereafter. Eventually, the employer is relieved of his responsibility to pay him wages as per the contract of employment. Hence, the payment of salary to the employee for the period of his absence is out of question.
Secondly, the act of unauthorised absence by the employee is a misconduct and his remaining so for long without further intimation,if any tantamounts to abandonment of employment.
Therefore, it would not be suffice on your part just considering him as a drop out and remove his name from the roll. You have to take disciplinary action against him as per the Standing Orders or the Service Reguations applicable to him by framing definite charges, conducting domestic enquiry, issuing second show cause notice etc addressed to him on his last known residential address available at your end and finally terminate him.