Can I claim economic compensation for not paying social security in full?

You can ask for financial compensation, but the reason for your resignation must be that the employer failed to pay social insurance premiums for you according to law, that is, the employer illegally employed. There is no legal basis for you to ask the employer to pay the social insurance premium, because both you and the employer are the obligatory subjects of social insurance premium, and the non-right subject, the social insurance premium collection unit is the right subject. Whether to ask them to pay back is decided by the social insurance fee collection and management department.

Legal objectivity:

Article 47 Calculation of Economic Compensation The economic compensation is paid according to the standard that the laborer pays one month's salary for each full year of working in this unit in People's Republic of China (PRC) Labor Contract Law. For more than six months but less than one year, it shall be counted as one year; If it is less than six months, economic compensation of half a month's salary shall be paid to the workers. If the monthly salary of workers is three times higher than the average monthly salary of local workers announced by the people's government of the municipality directly under the central government or the city with districts where the employer is located, the standard for paying economic compensation to workers is three times the average monthly salary of workers, and the longest period for paying economic compensation to workers shall not exceed 12 years. The monthly salary mentioned in this article refers to the average salary of workers in the twelve months before the dissolution or termination of the labor contract.