No and Yes.
For resignation to be effective, employees must be totally clear and unambiguous that their intention is to resign. You can’t, in other words, infer an employee is resigning the way an employee infer dismissal a la constructive dismissal. While I don’t know all the facts of this situation, I can tell you that employers who infer that employees are resigning without getting clarification are often hit with wrongful dismissal liability.
Recognizing that this is just a personal opinion and not legal counsel, which I’m not qualified to give, you have 2 basic choices: 1. Terminate yourself and provide the required notice; or 2. Ask the employee to determine what his/her intention is. Maybe you can work out a severance package that includes at least the employment standards minimums. There’s also the chance that the employee will terminate wrongfully, which would relieve you of your notice requirements. The one thing not to do is assume the employee quit and thus not pay termination notice. Hope that helps.