If you have mentioned effective date of resignation/notice period from date of notice of resignation and company discharges you before effective date of resignation it can be termed as illegal.
If you wish to accept early relieving amicably it is your choice.
You may obtain medical certificate also in addition to Rx of doctor, bed rest advice, diagnostic report e.g. lab report/ X ray report etc and signature and seal of doctor on all documents. Employee can submit sick leave application.
Paid leave can be encashed in FNF statement.
If your HOD and VP also are willing to approve leave ( any leave) take approval on leave application under signature by hand (seal if possible) and if workable and acceptable an email confirmation that leave is approved from dated...........to dated............ Do not leave anything to chances.
Employer can decline to approve other leave and can ask the employee to remain in seat and attend to process of completing tasks on hand, handing over the charge, transition to employee designated as replacement, etc.