This isn't necessarily true. Someone's income/credit might be too bad to get even a collateralized loan unless the bank makes a loan the homeowner obviously can't pay and then the bank taking posession of the house in a fairly short period of time. It's unethical to write a loan you know a person obviously cannot pay, even if it's just taxes.
The solution is simple though. Sell the house without taking posession of it and pay taxes based on the sale rather than on the assessed value when actually won. I'm not 100% sure if that can be done, but in today's market, there's no way the house is worth more than the value stated.
After the taxes are taken care of, use the remaining winnings to pay down debt and save any that's left and live in a home that is affordable.