Zakat is meant to help those in poverty, by distributing the wealth from those who have much more than they need, which is why most forms of Zakat are applied on those who have maintained more than a certain amount of money in their bank accounts.
There's a Nisab on Zakat which means that you have a minimum amount before you are obligated to pay Zakat. If your net worth would be negative, or below the Nisab amount, you're not obligated to pay (Zakatguide.org).
c) In long term, instalment debts, like housing instalments, and other debts that finance fixed assets, which are not counted for Zakat, the payer deducts the amount of annual instalment all at a time, then calculates the total sum of the remaining property and pays Zakat on it if it reaches the Nisab of Zakat.
For example, someone might have US$100,000 in their bank account (which is above the Nisab level) and holds a $200,000 loan. They pay $15,000 of that loan a year.
The debtor would have to pay Zakat on their $85,000 (savings minus installments) in their bank account, despite having a negative net worth. Which would mean that they pay $2,125 of Zakat (2.5% of $85,000).
On the other hand, let's they were to pay $98,000 off their loan off that year, leaving them with a loan of $102,000. This puts their savings at $2,000 (below the Nisab level). They wouldn't have to pay Zakat on this, despite having the same net worth.
This is to the best of my understanding; if someone can confirm or correct this, it would be helpful.