Debt Insurance

I have looked a a few threads here at MoneySavingExpert (MSE) and it is often claimed that when somebody defaults on a loan / credit card / contract or whatever, that the debt is covered by insurance. But in the same messages it is claimed that the debts are sold to debt collection agencies (DCA).
I find this totally implausable
Surely if the debt was covered by insurance then it would be illegal to sell the debt to a DCA as this would in effect be insurance fraud as the lender would of been paid twice for the same debt and the company would of claimed insurance agains a debt that had beed paid by the DCA.

Surely IF any debts were covered by insurance then Only the insurance company can appoint a DCA in an effort to recover what they paid