So I did some searching around with regard to this situation in Japanese and came across this information (which I translated from Japanese to English):
Precautions for those who change from spouse visa to permanent resident visa
Those who wish to apply for a permanent visa or permanent residence from a visa such as a Japanese spouse or a spouse such as a spouse or a permanent resident of the permanent resident may not only have pension for your own pension, Let's check it!
Although it is unexpectedly a blind spot, even if there is no delinquency or non-payment of the pension to the applicant himself / herself, there are cases in which the spouse is not paid due to the unpaid delinquency of the pension.
Even Japanese people have surprisingly many people who do not know their pension situation.
In the time of a student, or during the period when he was changing his / her job, he / she must join the national pension during the period when he / she is not employed (during the period when he / she is not a member of the employee's pension), but as soon as he / she has decided to re-hire it, the procedure of the national pension It is common that pensions are unpaid delinquent while you do not even know yourself, such as not doing.
So we encourage you to check your spouse's pension status before applying for a permanent visa if possible!
Even if you are currently a member of the pension, please contact the nearest pension office if there is a period (unpaid period) that you have not paid before working for the company or during the student days. We think that we can apply for pension payment or exemption for pension in unpaid period and delinquent period so we recommend you to confirm before applying for permanent visa.
Do I need pension documents when applying for permanent residence visa?
Since it is not required as a document required for immigration visa application from Immigration Bureau, it is not necessary to prepare at the time of application. However, according to recent trends, it is also good to prepare in advance because it is required for materials that understand the status of subscription and payment of pension as an instruction of additional documents. Also, if you have unpaid or unpaid delinquency, we recommend that you consult with your nearest pension office in advance. http://visa-immigration.net/info/pension