No word game here. It's a simple question. (And a question you chose to complicate by adding bankruptcy to the equation.)
By 'forgiving' the debt, the borrower came out $10K ahead. Who ended up paying that $10K (i.e. who took the loss)?
They turned an asset over to the bank with the promise that the asset would be repaid with interest. When that asset was not paid back as promised, that asset became a loss to the investors. The CD holders in essence took a loss of $10K.
Now let's remove bankruptcy from the equation and return to the original scenario. Let's say the bank had additional assets to repay the CDs with interest. Then the loss would be incurred by the bank itself. In other words, "wiping it off the books" involved the bank losing $10K. So the bank paid off the loan.
No, they purchased a certificate of deposit. That is what they paid for. The fact that they did insufficient due diligence, and ended up losing their investment because the bank lost its only asset does not mean that they paid for that asset. It means that they bore the economic risk of loss of the bank's assets and investments - which is precisely the same as saying that they purchased a financial asset with a counterparty that had a known nontrivial risk.
They did not pay for the loan.
That is about as imprecise - and as pernicious - as saying that a certain industry is racist because the racial mix of workers in that industry does not mirror the racial mix of society at large.
Now, if what you're trying to say is that the U.S. taxpayer is going to bear the economic consequences of the federal government cancelling certain student loans that, to-date, had stood as assets on its books, then I agree completely with you, but that is not because the taxpayers "paid" for those student loans.
Imprecise language is the devil's playground. I had always assumed that we here at TBR were a little better than that.