Sell the house, or pay off the mortgage?

My parents bought a home on a first time home buyers program in 1999. Part of the mortgage agreement was that the buyers of the home (my parents) could only sell the home to other buyers in the first time home buyers program until 50 years after the original sale of the home, and the home could only be sold at the price determined by the county. My parents agreed to the terms because they never thought that they would have any reason to move and because they thought the program was the only option they had if they wanted to own a home.

In 2009 my parents got behind on the mortgage payments and began working with Bank of America on a loan modification. After initially being accepted they were declined and the past due payments that originally totaled 5 thousand dollars now equal 20 thousand dollars.

However my question is not about loan modification though. Recently my grandmother passed away and left all her money to my father and my uncle. My parents now have enough money to pay off the mortgage in full (which they want to do so they can have more money each month to save etc.) but my question is: should they? Considering they can’t sell the home for any real profit in the future, shouldn’t they just sell the home and buy another house? And if they do sell the house, are they still on the hook for the 20 thousand in late fees and interest?
Yes it is 50 years. I read the agreement between the county and my parents. I know it sounds messed up, but it is the reality.

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