No. Normally, no employer will send an email asking the employee to resign because if they do so, it will become evidence that the employee has been asked to leave. Instead, the employer will only tell the employee verbally that they should go. Once the employee submits their resignation, it is regarded as an initiative from the employee to leave. Then there are no legal issues involved, and the employer can settle the accounts, which shall include salary and the leave balance, whatever is available.
Employer's Misunderstanding
But your employer or HR is being unreasonable. They are asking you to resign and at the same time saying that in records it would be construed as termination, and on termination, the employee is not paid any leave balance. The latter part is against the law, anyway, and it will not work as per their decisions. The former part, that resignation will be treated as termination, is unreasonable. When an employer is not happy with an employee, they can ask them to leave. They should have the courage to terminate the employee after following the protocols involved. No law states that an employer should keep a non-performing employee in service. They can terminate them, but it should not be done abruptly. The employee should be given at least a reasonable opportunity to improve their performance. For that, the employee will be put under a Performance Improvement Plan (PIP). After a few months, say six months, if the performance is still lacking, the employer can terminate them by paying as per the provisions in the contract of employment or the certified standing orders.
Employee Benefits and Resignation
Normally, when the employee is ready to leave, whatever benefits are payable will be paid in full. There will not be any bargaining. Simply, if the employee who is to be eliminated is ready to go, they will not look into other issues but will just allow them to leave. They cannot have their cake and eat it too. Your employer wants to eliminate you but will not compromise on compensation or other payments. That is why I said your HR is being unreasonable.
You should not expect HR to send an email saying that you should resign. But if you do not resign, they can send a termination letter. Again, you can defend that termination by contesting it, saying there is no reason for termination. As far as possible, avoid termination. It will lead to unpleasant situations for both you and the company. The company will, in turn, take it against you and spoil your career. Therefore, it is up to you to decide whether you should fight for the leave surrender salary and potentially spoil your career or just leave it and find another job.