This is a debt collection scam, pure and simple. First, they can't get the "DA" involved - owing a debt is not a criminal act. Assuming the SOL hasn't run on the debt (it depends on a few factors), they certainly can sue you, obtain a judgment, and try to collect. Other than that, there isn't anything else they can do. If you tell them you cannot be contacted at work, those calls should stop as well. Demand their address and send them, in writing, a letter demanding verification of the debt. If they won't do that, then they are in violation of federal collections laws.
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If the debt is more than EXACTLY six years old, you owe them nothing. Your remedy then is the federal Fair Debt Collection Act, which bars harassing people over uncollectable debts. Under no circumstances should you pay this over the phone.
As for the criminal charges, it is illegal to threaten someone with criminal prosecution to collect a debt., collectable or not collectble That is already a FDCA violation, and there are statutory damages of $1,000 per violation, plus any actual damages. Contact me if you want to consider demanding money from them.