Why don't foreigners working in Singapore pay social security?

Because you didn't sign a formal labor contract, there is no tax number.

Singapore social security provident fund CPF is the CentralProvidentFund, which is translated into central provident fund in Chinese. This is a social security savings plan established by the Singapore government for all Singapore citizens and permanent residents, requiring each participant to pay monthly. According to the age of employees, the provident fund will be transferred to different accounts according to different proportions. Generally speaking, the older employees are, the higher the proportion of medical accounts will be. Ordinary accounts are mainly used for daily needs, such as house purchase, investment, education and retirement. The medical account is mainly used for medical needs, and can be used to pay for inpatient bed fees, outpatient fees, operation fees, treatment fees and health care fees in some approved hospitals.