Clause 3, Article 116 of the Labor Code 2012 contains provisions on personal leave and unpaid leave as follows: An employee may discuss and agree with the employer on unpaid leave in addition to the leaves specified in Clauses 1 and 2 of that Article

Thus, you can discuss with your employer to take unpaid leave.

Regarding your participation in social insurance scheme, based on the provisions at Point 1.7, Clause 1, Article 38, Section 2 of Decision 959/QD-BHXH regulating the management of collection of social insurance, health insurance, unemployment insurance premiums; and the management of social insurance books and health insurance cards:

The employees who do not work and get paid for 14 working days or more in a month shall not have to pay the social insurance premium of such month. This period is not calculated for entitlement to the social insurance benefits, except for leave to enjoy the maternity benefits.

Accordingly, if you apply for unpaid leave for more than 14 days in a month, you are not subject to compulsory social insurance.