Hello and thank you for your question.
I'm not certain what you mean by "pay your Social Security tax until your birthday"
Can you please elaborate?
I guess I mean continue to pay into it even if I am not working.
If you are required to pay into the Social Security system because you are a wage earner or you are self employed, you must always pay into the system
This is true even AFTER you retire.
Ifyou are 83 and working for Wal-Mart as their employee, you sill pay into the Social Security system
You will be, in effect, funding part of your own retirement.
However, your benefit is re-evaluated annually. If you work enough such that it represents one of the highest 35 YEARS of income, then your benefit may nudge up slightly. It will never go back down.
If you retire in January, then you will not be working in Feb-Apr, so there is nothing to pay in.