Will social security be put on file by individuals or units after resignation?

If the company resigns and stops paying social security now, should it file a case by itself or by the company? Can social security pay it by itself and find a new company?

Yantai City Labor and Employment Office replied: If the unit individual resigns or terminates the contract, the individual will be responsible for putting on the file after the unit stops issuing insurance. You can pay insurance (only pension and medical insurance). For details, please contact the Labor Affairs Agency Section of the local Labor and Employment Office for consultation.