No show during notice period

We have an employee who did not turn up for work for a week giving reasons that he had injured his back.  Subsequently, he sent a resignation letter via email.  He promised to serve his 1-month notice as he had consumed all his leave.  However, he did not show up at all after the resignation letter.What action can the company?  Can we sue him for the notice in-lieu?
First, is your employee applying for Urgent Leave or Medical Leave for the 1-week absence from work?
If he called in for urgent leave, he is obliged to produce supporting document as Employer reserved the right not to approve urgent leave due to operation constraint.
If he called in for medical leave, he ought to submit his medical certificate.
In view of his resignation letter submitted and he AWOL* despite mentioning about his willingness to serve the 1-month notice. (Please confirm whether he called in to inform leave during this notice period and you may reject all leave application, even for medical leave application unless he is able to provide you with a genuine medical certificate). He shall be dismissed due to AWOL for more than 2 working days. In which, the employer may demand 1-month salary notice-in-lieu from the employee.
*Absence without official leave approval