By now your company must have reported the matter to the police. The police will have their own investigation for the causes of the suicide.
By the way, after death you cannot "terminate" an employee. A person who has terminated his life, how can you terminate him from the job? In simple words it is death of the employee. It appears that zeal of terminating the employees is so strong that few HRs do not want to spare the dead employee as well.
In the meanwhile, you may conduct security investigation from your side too. Let your security officer assisted by another manager make a list of the personal belongings of the deceased employee, collect these together and keep in the safe custody. These need to be handed over the nominee of the employee once the police investigation is over. Even while making list of the belongings also, it is better to involve the nominee of the deceased.
HR department may issue circular to all the departments to find out whether deceased employee had any dues against him or was allotted any company property (like laptop, mobile phone etc) to him. HR/Admin department may take over the company assets from his residence. Later HR department may take clearance on his behalf from all the departments and find out what are the dues against him.
In this FnF, you may pay him salary till his last working day, gratuity if applicable. Deduct dues if any, from this amount.
Assist nominee of the employee in getting PF/ESI benefits, as applicable. Provide assistance to the family of the deceased to claim death insurance benefits from insurance companies, credit companies etc. But before that the most important job is to get death certificate. Help the family of the deceased to get this certificate.
1st July 2017 From India, Bangalore