They’re not illegal, but a reputable lender wouldn’t write one. The risk of property value decreasing as the loan balance increase would make it extremely risky. You wouldn’t think of buying a home that’s worth less than the asking price.
There were some loans written a few years ago that were negative amortization loans with the expectation that later, you’d be able to catch up. Catch up didn’t happen.
Although the real estate crisis now was not brought on by negative amortization, the resule is the same. Houses were selling for much more than they were worth, market collapsed, now homeowners are negatively amortized (house worth less that loan balance).
If the apraised value of the house is less than your current value, I don’t think you can get a rewrite.