The day I put $50,000 in a shoe box and handed it to a stranger

They're likely correct that they don't have the bill or any decent documentation, but that also means they may be on thin ice getting anything from you, if you know your rights. (Or at least that seems to be true in the US; I'm not a lawyer and you should probably seek advice about your specific situation.)

From: Credit card debt collection

Debts are conveyed to the debt buyers as large CSV files with minimal supporting documentation. The legal reality of a credit card debt begins with a contractualized promise to pay. You might assume that the owner of the debt necessarily has read that contract. Reader, if the debt has been sold, they have not merely not read that contract, they have likely not received a copy of that contract. They might have the contractual right to ask the seller of the portfolio to ask the entity it bought the portfolio from to follow a few more links in the chain to eventually ask the financial institution for a copy of the contract. In principle, financial institutions always have the contract… somewhere. In practice, they will frequently not organize themselves to actually locate it; this business is off their books and Operations has better things to do than hunting in the archives for a paper copy of a low-value contract signed several years ago.

The rights of debtors are observed by both primary lenders and eventual debt buyers mostly in the breach. One of those rights is to a written “debt verification”, with specified information in it, and (surprisingly, if you haven’t worked in this field) despite that being the law many debts are sold in such a fashion that the buyer couldn’t produce a responsive verification even if they wanted to. That isn’t even a political claim; it’s just the engineering reality of which columns are in their CSV file.

The former advocate in me will observe that the single most effective method for resolving debts is carefully sending a series of letters invoking one’s rights under the FDCPA (and other legislation) to a debt collector who is operationally incapable of respecting those rights, then threatening them with legal or regulatory action when they inevitably infringe upon them in writing, leading to them abandoning further attempts at collection.

This effectively makes paying consumer debts basically optional in the United States, contingent on one being sufficiently organized and informed. That is likely a surprising result to many people. Is the financial industry unaware of this? Oh no. Issuing consumer debt is an enormously profitable business. The vast majority of consumers, including those with the socioeconomic wherewithal to walk away from their debts, feel themselves morally bound and pay as agreed.

Also:

As a former advocate, I’d report that it is never in a debtor’s interest to verbally speak to a debt collector under any circumstances. One’s likelihood of being abused or lied to, including in financially consequential fashions, is high, and one’s ability to counter that is minimal. Instead, force them to do all correspondence on paper, where lies are self-documenting, illegal threats are immediately admissible to regulatory processes or court, etc.

And it seems that just taking a break is important, which hanging up and calling back later gives you a chance to do.