All they say is they are with the "Fraud Investigation Unit" and leave a phone number, never say what company they are calling from. Leave 513-330-8691 as a call back number.
Enough, PLEASE, Don't give advice when you have no idea what is going on, or what the law really is.
Pretending for a moment that this is a legitimate debt with a legitimate collector. Starting the conversation off with a C&D is a good way to get sued. A C&D, also known as a "drop dead" letter does not stop phone calls. It stops EVERYTHING. You are refusing to handle the matter with them. A real CA with a substantial and real collectible debt is probably going to reply to a C&D with a can of litigation whoopa$$. Why? Because you just ended ALL further discussion towards a settlement.
"Enough", Before you ever make another post, go memorize and understand everything you find here: <http://www.ftc.gov/os/statutes/fdcpajump.shtm>
At the moment, you seem to have NO understanding of the law, and that makes you a hazard to people who mistakenly think they know less than you do.
Now, let's assume that this is a phony collector with phony debt, which I suspect may be the case here. The next time they call, one might wish to tell them that you are familiar with the Fair Debt Collections Practices Act (you did go study the material I linked to, right?), that you believe that they may be a fraudulent operation, and if they aren't, they need to send you a validation letter. Tell them that until you get such a letter, there is nothing to discuss, and you will not take their calls. DO NOT give them your address, or any other information. Tell them to use the address they have in their records. If they persist, saying they don't have to do that, threaten you, etc.,. Tell them that they do not intimidate you in the least, and as far as you are concerned, unless they can validate the debt, they can go pound sand. Tell them you are recording all future calls, and if they persist in violating the FDCPA you will consult with your attorney. Then hang up. They may continue to call, in frustration they may even act worse than before, but if you ignore them, they will eventually move on to an easier target. Call blocking is also a good thing to consider.
Why not just send them a C&D if they are fakers? Because they are likely to ignore it, and you have just documented who you are and where you are for them. Besides, giving them a chance to validate follows the law, and lets you feel more comfortable about whether these are scammers.
For the rest of the answers, please go read the web FTC web site I linked. My answer is not comprehensive, and you must read the law for yourself. PLEASE.
When it they say they are the "Fraud Investigation Unit" they have violated the law. Read the FDCPA link I posted. These people are either bottom feeders dealing in junk paper, or outright phonies.