However, after the termination of labor relations, employees' identity is temporarily lost, and they do not belong to individual industrial and commercial households without employees, part-time employees who have not participated in the basic old-age insurance in the employer and other flexible employees, so they cannot participate in employee social insurance.
I can entrust others to pay social insurance premiums, but only if I am participating in social insurance. In the case that I have not participated in social insurance or stopped insurance, neither others nor I can pay social insurance premiums. After your mother's work unit terminated the labor contract, I believe she has also registered the reduction of social insurance personnel and handled the insurance termination procedures of your mother, so your mother can't pay the fee before re-registering the social insurance relationship.
At present, prisoners cannot apply for social insurance for employees. I'm afraid only after your mother is released, she will pay the basic old-age insurance premium of 15 years in accordance with the relevant provisions of the Social Insurance Law, and then go through the relevant procedures to apply for old-age benefits.