It's too good to be true. Sounds like there is a broken story there. That just does not happen. But to answer your question, anyone can call their insurance and ask them to write off their cars if they are looking to get laughed at.
I was in a similar situation with a Daihatsu where constant issues were killing me financially. I did what I could, but things kept breaking. I traded it in for a new Kia and didn't look back. But I essentially replaced the time and money I spent on problems with heavy monthly instalments and a lovely balloon payment. While it's a great car, and I still have it 6 years later, it's not all magic. I have had problems over the years, which mostly took a lot of time and negotiating to solve.
There is no magic solution I'm afraid. It sounds like your sister needs to either find a way to finance the shortfall, or make do with what she has until trade in value more or less matches the settlement amount. Fraud isn't the answer either.
You have done this forum a good service by warning us to stay away from those cars