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.
Without stating reasons for demanding resignation as rightly pointed out, any advice would be futile.
As true HR professional, you should examine the propriety of demanding resignation. Your query of whether to pay half salary or not is misconceived without the proper knowledge of terms of employment and grounds for resignation/ termination.
I am getting the impression that you are doing what you have been told to do without sharing your mind on the issue. May be I am wrong but you have to advise the management right action arising out of your own conviction supported by legality, ethics and best practice.Remember, HR is the 'conscience keeper ' of the organization.