You don't "own" your own debt. The bank / other entity you are indebted to "owns" the debt, hence why they can sell it to a debt collector for pennies on the dollar. Instead of owning your debt, you are liable (or there's a better word than "liable") for your debt. Basically, you already "sold" your debt when you first became indebted.

It's not really a dumb question. I get why people might look at their debt as something they own, given the debt itself is tied to their identity and credit score until paid off.