Hi,
You are referring about the performance issues during notice period only which will be very minimal say 30 days ? So his performance while on service was good ?
So why to deny FNF and relieving letter on that grounds.
You may deny relieving letter and FNF if the employee absconded from work without any information. You can justify the reason. But in your case employee submitted resignation and completed notice period. Obviously employee might not perform with full enthusiasm during notice period which is very much common.
Full and final Settlement can be holed /denied when there is a signification loss to the Company caused by the employee by any means. Even in that case it needs to be proved by the employer.