Hi,
Simply put, it's a toss up. The legal standard for debt validation is not defined very well, and the leading case law on the matter basically says "debt verification is nothing more than the debt collector confirming in writing that the amount due is correct." There is other case law though that contradicts that ruling, and some that have even said that the verification must be generated by the original creditor (like a copy of a bill).
One thing is for certain, you can write the collector back and say that what they sent did not satisfy you that there was a balance owing, and specifically request a copy of a final bill. They are under no obligation to give it to you, but if they can get it and think it will help make you pay then they may just do it. At minimum they would have to report it in your credit file as disputed if you tell them you continue to dispute.
Obviously I don't know anything about the alleged debt, but there is one good thing: in virtually no situation will that letter that says "yep, we verified it, it's right, pay up" prove anything in court if they intend on suing you - as long as you show up to defend (assuming of course they actually sue you). One would think that if they don't have anything more concrete than that to send you when you request validation, then they likely can't prove it in court either.
I wouldn't mention your financial situation, it won't do too much I'm afraid. If you want to pay it though, you could always write them back saying that you aren't satisfied with their verification as it doesn't prove anything to you, but in a good faith effort to settle the matter you'll offer them $xyz. I did this once and offered 20% of what they claim was owed.
They'll either accept it, counter it, or reject it. Just make sure that they know you will only pay if they agree to consider the matter Paid in Full afterwords, and get it in writing before you pay them. If they reported it to your credit report, you could negotiate a possible deletion of that as well. Just some options to throw out there.
Final note: Depending on the type of debt, the amount, and when the debt went bad, it could be time-barred and they may not even be able to sue you for it. Try doing some research on that if it's beneficial!
Good luck!