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Yes, they can come after you personally, but the likelihood of that is not very great. Usually, lawyers aren't interested in pursuing claims where there's no guaranteed (insurance) money available.
I wouldn't give an affidavit without first consulting with a local lawyer and making sure what you are dealing with.....and to make sure that you are not painting yourself into a corner.
That's what I would do before giving them anything....especially something that could be used against you.