The simple answer is "yes, although it isn't as clear when the issue is a miscalculation of monthly benefits and I have seen the agency, and the courts, rule both ways on this issue. When a benefit amount is awarded if you disagree with that amount then there is an appeal process to go through. Many times the agency and the courts will say that by failing to utilize the appeal process the claimant has waived any right to the past benefits. I've also seen the agency go back and recalculate and award a lump sum distribution for the amounts that were underpaid, award an increase in monthly benefits to allow the SSA to "catch up" on what should have been paid, or both. I have no idea why the SSA pays some and doesn't pay others and there doesn't appear to be any rhyme or reason.
This usually occurs with disability benefits, rarely with retirement or survivor benefits.
At this point the appropriate step to take would be to try and appeal the decision even though, technically, it is "out of time" for appeal. The Social Security publication has the following info on appeals:
"Right to appeal If you disagree with a decision made on your claim, you can appeal it. For an explanation of the steps you can take, read The Appeals Process (Publication No. 05-10041). You can handle your own appeal with free help from Social Security, or you can choose to have a representative help you. We can give you information about organizations that can help you find a representative. For more information about selecting a representative, read Your Right to Representation (Publication No. 05-10075)."
In this case, the appeal should work if she argues that the mistake wasn't discovered until the SSA revealed it and therefore she should now be able to appeal the original amount and receive the underpayment. The Code of Federal Regulations 416.542 specifically allows for her monthly amount to be increased to pay for an underpayment.
If the appeal doesn't work, then the next step would be to file a lawsuit in federal court and, of course, she would need a lawyer to help with that since it is extremely complicated.
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Of course, please feel free to ask any follow up questions in this thread.