If this is the case, then there is another angle you can play.
They already told you they cannot locate their records. One of YOUR RIGHTS as a debtor under law is to demand "debt validation", meaning that a "billing statement" would not do, but only evidence of what the debt is would do. They would need documentation to uphold the original debt, and I have read many cases collection agencies bring to court gets thrown out because they can't obtain "debt validation". But what they still do though is they would sue you hoping in your case, you are so scared, disorientated, and concerned "you don't have any paperwork", don't show up, and they get a default judgement.
But wait. They are supposed to have the paperwork, and because they told you they don't have it, so your best solution is to demand they come up with it. It is their job to come up with it, NOT YOU.

