Hi Rasika,
Paying half salary to an employee with full attendance for the month would not be legal and yes it can have consequences where the employee can easily lodge a complaint on exploitation.
I am not sure on what grounds the employee has been asked to resign. So, I may not be able to provide a detailed answer. If the resignation has been asked for, based on performance or disciplinary grounds, and if the employee refuses to resign, then it is better to proceed on the full inquiry and share the findings with the employee for proceeding on termination if the evidence is intact. This usually is a difficult process.
If you could let us know the reason for why the employee has been asked to resign, we can look into this.