I didn't say anything about what he has lost, I asked the question what is he worth. Using your house example, at the point you ask the question I have an asset worth $50,000, i.e. the house, and a liability of $90,000, i.e. the mortgage. Therefore my net worth at that point in time is -$40,000. My gross worth is $50,000. What is Trump publishing? His gross worth, i.e. ignoring liabilities, or his net worth, taking account of his liabilities. The suspicion is that he is only ever publishing his gross worth, i.e. ignoring liabilities.
To return to your example, I am faced with a choice. I could walk away from the house and default on my liability. If I did that I would have lost $10,000, i.e. my original equity in the property, and have a net worth of zero. I would have stiffed the bank and they would have lost $40,000 on that particular asset. I suspect the bank wouldn't simply accept that outcome and would probably pursue me through the courts for their loss. In that case the court might well grant them a lien on a percentage of my future earnings. Since they would probably be allowed to accumulate interest on the debt at some court approved rate I could finish up paying off that debt for the rest of my life.