Yes, you should request verification. However, understand what the proper response is to verification. They only need to tell you the name of the original creditor, that creditor's address, and the balance due. Note, even if they don't verify, it doesn't mean you are off the hook. The debt is usually just passed to another collection agency.
No harm in making them jump through a few hoops.
Ultimately, to recover and rebuild, you need to be proactive about solving the debt problem. That could mean bankruptcy, or possible some other option depending on the circumstances. However, bankruptcy should be the FIRST choice because it is almost always the least costly option that brings the most certainty to a result.
I agree with my colleagues and would add that you should keep in mind that if the creditor does verify your debt, it may speed up litigation against you since they may decide that they have the necessary documents to prove that you owe this debt in court. You should call an attorney as there are many factors involved.
If you know the debt to be legitimate, then making the debt collector verify the debt is the equivalent of a temporary roadblock. Once the debt is verified, the collection agency can add interest and other fees to your bill depending on the circumstances of your particular account. You should get your debt discharged or settled.
If you request debt verification within 30 days of the initial contact with the collection agency, the agency must cease all communications with you until they provide you with validation. If they continue to call you before they send validation, they would be in violation of the Fair Debt Collection Practices Act (FDCPA) and you would be entitled to damages. Your request must be in writing and must be within the initial 30 day period; otherwise it will have no effect. It takes very little to comply with a debt verification request - the agency only needs to provide you with the name and address of the creditor.