Well people do take on debt for things that are quickly worth nothing. For example, you buy groceries with a credit card. You eat them; they are gone. But you still have the debt.

Or you buy a car. It quickly loses value, but you still have the debt based on the original purchase.

The formula still holds, but the "equity" part is negative, which leads many people to conclude that bankruptcy is a better option than paying for something they no longer have or is no longer worth what they owe.