I will give you general information since I do not know the specifics of your case. In order to win the law firm would have to prove: 1) knowingly "pirating" software; 2) that the software was not purchased; 3) that the statute of limitations in your state has not passed; and 4) damages.
They, bringing the case against your company, have the burden of proof. That means that they must prove all of the items that they are claiming by a preponderence of the evidence, or, in other words, that they prove their allegations are "more likely than not". What are your defenses? Was the software purchased from a reputable seller, can you call the seller as a witness? What is the statute of limitations in your state? Does the BSA have any defenses to a statute of limitation argument? What have their damages been?
The more proof you have to defeat these allegations the better you will be in negotiations. If you have a legal department, have them investigate these issues. If not, please consult with a contract lawyer in your state and ask him/her these questions and how to mount a capable defense. Then, after that is done, your attorney can send a letter telling the BSA to stop. The first step is to investigate this and get all the documentation that you can to support your case.
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