Criminal cases are different from administrative and political security cases. After the case is filed, the case must be suspected of receiving relevant legal penalties before it can be closed. Being private cannot be the reason for closing the criminal case. In other words, if an individual is private, the Criminal Investigation Brigade cannot officially Case filed and closed.
The "General Principles of the Civil Law" stipulates that civil acts that violate the law or social and public interests are invalid.
So criminal cases cannot be kept private legally, and I personally do not recommend keeping them private, because these cases will involve many problems in the future.
Because this type of private agreement has no legal effect, if the victim takes the parties to court in the future, everything done now will be in vain.