The debt collector tells the debtor that he owns around $20,000. I wonder that debtor could offer $500 to avoid that in his credit score. I guess the debt collector is better of by taking the $500 instead of nothing. How long will that stay in the report?
The creditor will take your $500 and still report the debt anyway - so long as the information reported is factually correct, it can be reported. So, your $500 payment would reset the clock on reporting the debt and on suing you for the unpaid balance. Unpaid debt can be reported for up to 7 years from the last date of activity on the account.
An unpaid debt will be reported 7.5 years from the date of first delinquency (DOFD) and 7 years from the date of last activity (DOLA), assuming both are calculated properly.
Even if you were to pay 100% of this debt to the collector, the collector is obligated by its deals with the credit reporting agencies to merely mark the debt as paid, not delete the negative tradeline. Nonetheless, consumers do sometimes obtain "Pay for Delete" from their creditors (which is improper in the context of the creditors' relationships with the CRAs, but that's not your problem).
What *is* your problem is that the creditor can of course sue for the $20k. And in many cases, the creditor will win the case and obtain a judgment. However, that isn't always the case, and there are techniques to mitigate the damage or even obtain a complete victory.
If you face debt collection you may choose to fight it and defend against garnishment. You may also seek debt settlement as a way to negotiate with creditors.