Is it permissible for a retiree whose pension is insufficient and who owns money in stocks and is a tenant to register for social security?

The ruling on subscribing to social security is explained in Fatwa no. 102456. The permissibility of registering for social security is tied to the social security regulations that define those who are eligible. So, if the conditions apply to you, then it is permissible for you to take from it; otherwise, it is not. You should consult social security officials regarding this matter.