Typically, the charge-off would be the difference between the original face value of the debt and the price it was sold to the debt collector.
The debt collector's tax basis is the price they paid for the debt. If they fail to collect the debt, there is a net loss equal to what they paid for the debt. This tax loss can be set against other debts that are recovered (profits).
If the full face value of the debt is recovered, the debt collector owes tax on the difference between their basis (what they paid for the debt) and the amount collected from the debtor. Of course, this profit is set against the losses on the remainder of the debt portfolio, so the net tax owed is the cumulative debts collected above the basis, less the loss on uncollected debt.
The debt collector's tax basis is the price they paid for the debt. If they fail to collect the debt, there is a net loss equal to what they paid for the debt. This tax loss can be set against other debts that are recovered (profits).
If the full face value of the debt is recovered, the debt collector owes tax on the difference between their basis (what they paid for the debt) and the amount collected from the debtor. Of course, this profit is set against the losses on the remainder of the debt portfolio, so the net tax owed is the cumulative debts collected above the basis, less the loss on uncollected debt.