Assuming the collection agency is a "debt collector" under the Fair Debt Collection Practices Act, you have rights. Threatening to have someone arrested for a debt is harassment. The collection agency should send an initial written notice with information about the alleged debt. You would have 30 days from receipt of the notice to send a written dispute of the debt. The collection agency must then cease its collection efforts until it provides "validation" or "verification" of the debt. Because of the deadlines and technical requirements, you may want to speak to a lawyer who's familiar with the FDCPA.
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I have seen severalof these kinds of threats from "collectors" recently. The contacts they have with consumers are filled with over the top viollations of the FDCPA, like the ones you mentioned. Two things. Sketchy lenders use sketchy collectors. Also, a couple of years ago, there was a story of some payday lenders having their computer files hacked. It could be that these folks are scammers and have obtained your information through that means. You should contact a qualified consumer attorney in your area tosee if there is anything that can be done.