So if you sell a note to someone they have no right to collect?
If you sell a note to someone, you are using the debt as the thing you are offering for sale. Once you sell the note, you've terminated the debt. After all, can you then go collect on the debt? Nope. So you, as creditor, are out of it. You have received payment for it - for your right to collect on an actual, verifiable, debt.
Selling a debt is confused with transferring a debt. If you are a creditor and you sell your business, or die and transfer your assets to your heirs, you haven't sold your debt. Those new entities actually own the original debt instrument, and collect on it, because they have assumed the status of the creditor.
If you sell a debt, however, you are abandoning your efforts to collect it from your debtor. THEN you are actually using the debt instrument as an item of sale that literally destroys your claim to its original agreement. That's what you are actually getting paid for - to destroy the debt. Thus, you are terminating your contract with your debtor.
What the buyer, the debt collector, is purchasing, is protected status under debt collection laws that protect them from fraud and extortion charges if they follow debt collection rules, as well as some rights to attempt to collect money based on that terminated debt instrument.
But they are not, in any way, buying the debt itself. Because the creditor agreed to settle that debt by literally selling their right to collect on it. And when they did that, the debt no longer existed.
It's confusing, because if the creditor did not sell the debt, but instead sued the debtor, they would follow the same claim in court that the debt collector does. The problem is that the law allows the court to let the debt collector act as if they are the creditor if they "buy" a debt, and only requires the debt collector to prove their creditor status if challenged by the person they are suing.
You can do the same thing. You can sue a perfect stranger, and unless they refuted you and demanded to see where they agreed to pay you anything, you could produce any fraud to support your suit - who would know? But in the case of debt collectors, they are institutionally protected by the simple fact that people don't know the law. And that is what they are really buying when they buy debts - the appearance of legitimacy, and the guarantee of limited liability under the law.
Note - this doesn't mean people don't have to pay their debts. Actual creditors CAN go after debtors, and NONE of this applies. This is just about debts that have been "sold" to debt collectors.