In other words, $350k home = $300k mortgage + $50k in equity. You still have debt. Its just that the debt was exchanged for something. Its the same equation for credit card debt.
No one takes on debt without receiving something in return.
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.
Aside from perhaps the first year of owning a financed car, it is worth more than remaining principal on the loan for the majority of the loan's duration.