In this case an employee is effectively absent without leave and the best way of dealing with it is to write to the employee stating that you need to know why they are not attending work. Give them a date by which their reply must be received and explain that if they don’t either attend work or give a good reason for their absence, you will treat it as a resignation.
If the date for their reply lapses without a positive response, a follow up letter can confirm that you have treated their continued absence without leave as a resignation.
It is advisable to offer the opportunity of an appeal but effectively, as of the date of delivery of your letter confirming you have accepted their resignation, their employment has ended. Send both letters by recorded delivery so that you can prove they were sent to the last known address.
From a contractual point of view, the employee is in fundamental breach of the employment contract because they have failed to provide their labour as required by the contract.