The law is very specific about the requirements for exemption from the Social Security program, and most taxpayers do not qualify. But yes, exemptions do exist for a small number. Certain religious groups, students, U.S. citizens who decide to forfeit their national citizenship, employees of foreign governments and self-employed workers who make less than $400 annually are all examples of taxpayers who are not responsible for paying Social Security taxes. Of course, since they are exempt, they are also ineligible to receive any Social Security benefits.
Other groups pay a limited amount, including individuals and couples making an income above a designated threshold specified by the IRS. Their additional income is taxed at a reduced rate under the Social Security system, reducing the overall Social Security tax liability of high-income taxpayers.
Social Security benefits are available only to taxpayers who either are contributing taxes to the system or did so in the past. Benefits are paid monthly to retirees, disabled individuals, surviving spouses and others. These programs include direct cash benefits, payments to surviving family members in the event of the enrollee's death and assistance for people with documented disabilities who are unable to continue working. Most of the individuals receiving Social Security are retirees, who paid taxes that supported these programs during their careers and now receive a monthly check themselves.
Social Security is a pay-as-you-go system, with current workers covering the costs of benefits provided to current recipients. The Social Security program automatically enrolls most U.S. workers, and enrollment is connected to the Social Security numbers of workers and taxpayers within the U.S. All Social Security benefits were created as part of a social safety net designed to reduce poverty and provide care for the disabled.
Officially joining an exempt group may require an application to the IRS. Taxpayers who wish to qualify for a religious exemption usually have to apply and specifically ask the IRS for an exemption from paying self-employment taxes as well. The IRS grants exemptions to ministers, members of the clergy and Christian Science practitioners on a regular basis, for example. Individual members of religious orders who have taken a vow of poverty are automatically exempt from self-employment taxes and Social Security taxes by default, but others must obtain specific permission from the IRS.
As these examples demonstrate, becoming exempt from paying Social Security taxes requires specific action by the taxpayer and special permission from the IRS. There is no legal way to stop paying Social Security taxes, in other words, without applying and receiving approval or becoming a member of a group that is already exempt.