My wife was a county employee for 23 years and never paid SS taxes since her former employer has or had its own retirement fund for its employees. When she was terminated from her job, she applied for SSDI. It was rejected because she has not earned a total of 40 credits (required to be eligible for SSDI). She already has earned 20 credits from old jobs so she needs 20 more credits to go. She was very upset so she had to find another job that pays SS taxes.
So my point is that not everyone who works pays SS taxes (since someone in this thread said that everyone who works pays SS which is not always true). EX: self-employed people, county or city employees in some areas, workers at private businesses that pay under table, etc.
I am a USPS employee for 27 years and I pay SS taxes (old name-FICA) and even Medicare taxes that was added about 10 years ago (I don't remember exactly when).